Analyzing data in complicated 3D domains: Smoothing, semiparametric regression, and functional principal component analysis

In this work, we introduce a family of methods for the analysis of data observed at locations scattered in three-dimensional (3D) domains, with possibly complicated shapes. The proposed family of methods includes smoothing, regression, and functional principal component analysis for functional signals defined over (possibly nonconvex) 3D domains, appropriately complying with the nontrivial shape of the domain. This constitutes an important advance with respect to the literature, because the available methods to analyze data observed in 3D domains rely on Euclidean distances, which are inappropriate when the shape of the domain influences the phenomenon under study. The common building block of the proposed methods is a nonparametric regression model with differential regularization. We derive the asymptotic properties of the methods and show, through simulation studies, that they are superior to the available alternatives for the analysis of data in 3D domains, even when considering domains with simple shapes. We finally illustrate an application to a neurosciences study, with neuroimaging signals from functional magnetic resonance imaging, measuring neural activity in the gray matter, a nonconvex volume with a highly complicated structure.

Nonlinear function-on-scalar regression via functional universal approximation

We consider general nonlinear function-on-scalar (FOS) regression models, where the functional response depends on multiple scalar predictors in a general unknown nonlinear form. Existing methods either assume specific model forms (e.g., additive models) or directly estimate the nonlinear function in a space with dimension equal to the number of scalar predictors, which can only be applied to models with a few scalar predictors. To overcome these shortcomings, motivated by the classic universal approximation theorem used in neural networks, we develop a functional universal approximation theorem which can be used to approximate general nonlinear FOS maps and can be easily adopted into the framework of functional data analysis. With this theorem and utilizing smoothness regularity, we develop a novel method to fit the general nonlinear FOS regression model and make predictions. Our new method does not make any specific assumption on the model forms, and it avoids the direct estimation of nonlinear functions in a space with dimension equal to the number of scalar predictors. By estimating a sequence of bivariate functions, our method can be applied to models with a relatively large number of scalar predictors. The good performance of the proposed method is demonstrated by empirical studies on various simulated and real datasets.

Segmentation of the aorta in systolic phase from 4D flow MRI: multi-atlas vs. deep learning

OBJECTIVE

In the management of the aortic aneurysm, 4D flow magnetic resonance Imaging provides valuable information for the computation of new biomarkers using computational fluid dynamics (CFD). However, accurate segmentation of the aorta is required. Thus, our objective is to evaluate the performance of two automatic segmentation methods on the calculation of aortic wall pressure.

METHODS

Automatic segmentation of the aorta was performed with methods based on deep learning and multi-atlas using the systolic phase in the 4D flow MRI magnitude image of 36 patients. Using mesh morphing, isotopological meshes were generated, and CFD was performed to calculate the aortic wall pressure. Node-to-node comparisons of the pressure results were made to identify the most robust automatic method respect to the pressures obtained with a manually segmented model.

RESULTS

Deep learning approach presented the best segmentation performance with a mean Dice similarity coefficient and a mean Hausdorff distance (HD) equal to 0.92+/- 0.02 and 21.02+/- 24.20 mm, respectively. At the global level HD is affected by the performance in the abdominal aorta. Locally, this distance decreases to 9.41+/- 3.45 and 5.82+/- 6.23 for the ascending and descending thoracic aorta, respectively. Moreover, with respect to the pressures from the manual segmentations, the differences in the pressures computed from deep learning were lower than those computed from multi-atlas method.

CONCLUSION

To reduce biases in the calculation of aortic wall pressure, accurate segmentation is needed, particularly in regions with high blood flow velocities. Thus, the deep learning segmen-tation method should be preferred.

Libkrylov: A modular open-source software library for extremely large on-the-fly matrix computations

We present the design and implementation of libkrylov, an open-source library for solving matrix-free eigenvalue, linear, and shifted linear equations using Krylov subspace methods. The primary objectives of libkrylov are flexible API design and modular structure, which enables integration with specialized matrix-vector evaluation "engines." Libkrylov features pluggable preconditioning, orthonormalization, and tunable convergence control. Diagonal (conjugate gradient, CG), Davidson, and Jacobi-Davidson preconditioners are available, along with orthonormal and nonorthonormal (nKs) schemes. All functionality of libkrylov is exposed via Fortran and C application programming interfaces (APIs). We illustrate the performance of libkrylov for eigenvalue calculations arising in time-dependent density functional theory (TDDFT) in the Tamm-Dancoff approximation (TDA) and discuss the convergence behavior as a function of preconditioning and orthonormalization methods.

An Optimization Approach Coupling Preprocessing with Model Regression for Enhanced Chemometrics

Chemometric methods are broadly used in the chemical and biochemical sectors. Typically, derivation of a regression model follows data preprocessing in a sequential manner. Yet, preprocessing can significantly influence the regression model and eventually its predictive ability. In this work, we investigate the coupling of preprocessing and model parameter estimation by incorporating them simultaneously in an optimization step. Common model selection techniques rely almost exclusively on the performance of some accuracy metric, yet having a quantitative metric for model robustness can prolong model up-time. Our approach is applied to optimize for model accuracy and robustness. This requires the introduction of a novel mathematical definition for robustness. We test our method in a simulated set up and with industrial case studies from multivariate calibration. The results highlight the importance of both accuracy and robustness properties and illustrate the potential of the proposed optimization approach toward automating the generation of efficient chemometric models.

Accelerating gradient descent and Adam via fractional gradients

We propose a class of novel fractional-order optimization algorithms. We define a fractional-order gradient via the Caputo fractional derivatives that generalizes integer-order gradient. We refer it to as the Caputo fractional-based gradient, and develop an efficient implementation to compute it. A general class of fractional-order optimization methods is then obtained by replacing integer-order gradients with the Caputo fractional-based gradients. To give concrete algorithms, we consider gradient descent (GD) and Adam, and extend them to the Caputo fractional GD (CfGD) and the Caputo fractional Adam (CfAdam). We demonstrate the superiority of CfGD and CfAdam on several large scale optimization problems that arise from scientific machine learning applications, such as ill-conditioned least squares problem on real-world data and the training of neural networks involving non-convex objective functions. Numerical examples show that both CfGD and CfAdam result in acceleration over GD and Adam, respectively. We also derive error bounds of CfGD for quadratic functions, which further indicate that CfGD could mitigate the dependence on the condition number in the rate of convergence and results in significant acceleration over GD.

Projecting XRP price burst by correlation tensor spectra of transaction networks

Cryptoassets are becoming essential in the digital economy era. XRP is one of the large market cap cryptoassets. Here, we develop a novel method of correlation tensor spectra for the dynamical XRP networks, which can provide an early indication for XRP price. A weighed directed weekly transaction network among XRP wallets is constructed by aggregating all transactions for a week. A vector for each node is then obtained by embedding the weekly network in continuous vector space. From a set of weekly snapshots of node vectors, we construct a correlation tensor. A double singular value decomposition of the correlation tensors gives its singular values. The significance of the singular values is shown by comparing with its randomize counterpart. The evolution of singular values shows a distinctive behavior. The largest singular value shows a significant negative correlation with XRP/USD price. We observe the minimum of the largest singular values at the XRP/USD price peak during the first week of January 2018. The minimum of the largest singular value during January 2018 is explained by decomposing the correlation tensor in the signal and noise components and also by evolution of community structure.

Group refractive index via auto-differentiation and neural networks

In this article, using principles of automatic differentiation, we demonstrate a generic deep learning representation of group refractive index for photonic channel waveguides. It enables evaluation of group refractive indices in a split of second, without any traditional numerical calculations. Traditionally, the group refractive index is calculated by a repetition of the optical mode calculations via a parametric wavelength sweep of finite difference (or element) calculations. To the direct contrary, in this work, we show that the group refractive index can be quasi-instantaneously obtained from the auto-gradients of the neural networks that models the effective refractive index. We embed the wavelength dependence of the effective index in the deep learning model by applying the scaling property of the Maxwell's equations and this eliminates the problems caused by the curse of dimensionality. This work portrays a very clear illustration on how physics-based derived optical quantities can be calculated instantly from the underlying deep learning models of the parent quantities using automatic differentiation.

The effects of atomic percentage and size of Zinc nanoparticles, and atomic porosity on thermal and mechanical properties of reinforced calcium phosphate cement by molecular dynamics simulation

This study used the molecular dynamics (MD) simulation method to assess the effects of different percentages of NPs, sizes, and percentages of porosity on reinforced cement thermal behavior (TB) and mechanical behavior (MB) of samples. The temperature and kinetic energy (KE) converged to 300 K and 35.42 eV after 10 ns, which indicated the thermodynamic equilibrium and the atomic stability in the structures. Increasing the NPs percentage from 1% to 3% increased the maximum temperature from 1364 to 1405 K. By further increasing it to 5%, it was reduced to 1361 K. As the radius of Zn NPs increased to 16 Å, the ultimate strength (US) and Young's Modulus (YM) increased from 1.07 to 0.19 MPa to 1.2 and 0.22 MPa. The increase in the NPs' radius to 16 Å caused an increase in the maximum temperature from 1405 to 1455 K, maintaining atomic stability. As the porosity increased from 1% to 5%, the US and YM reduced from 0.91 to 0.17 MPa to 0.81 and 0.15 MPa. As the porosity increased from 1% to 5%, the maximum temperature was reduced from 1400 K to 1384 K. According to the results, Zn NPs' percentage and size effectively improved the MB of the final cement.

Generative models and Bayesian inversion using Laplace approximation

The Bayesian approach to solving inverse problems relies on the choice of a prior. This critical ingredient allows expert knowledge or physical constraints to be formulated in a probabilistic fashion and plays an important role for the success of the inference. Recently, Bayesian inverse problems were solved using generative models as highly informative priors. Generative models are a popular tool in machine learning to generate data whose properties closely resemble those of a given database. Typically, the generated distribution of data is embedded in a low-dimensional manifold. For the inverse problem, a generative model is trained on a database that reflects the properties of the sought solution, such as typical structures of the tissue in the human brain in magnetic resonance imaging. The inference is carried out in the low-dimensional manifold determined by the generative model that strongly reduces the dimensionality of the inverse problem. However, this procedure produces a posterior that does not admit a Lebesgue density in the actual variables and the accuracy attained can strongly depend on the quality of the generative model. For linear Gaussian models, we explore an alternative Bayesian inference based on probabilistic generative models; this inference is carried out in the original high-dimensional space. A Laplace approximation is employed to analytically derive the prior probability density function required, which is induced by the generative model. Properties of the resulting inference are investigated. Specifically, we show that derived Bayes estimates are consistent, in contrast to the approach in which the low-dimensional manifold of the generative model is employed. The MNIST data set is used to design numerical experiments that confirm our theoretical findings. It is shown that the approach proposed can be advantageous when the information contained in the data is high and a simple heuristic is considered for the detection of this case. Finally, the pros and cons of both approaches are discussed.

Dynamic Precision Approach for Accelerating Large-Scale Eigenvalue Solvers in Electronic Structure Calculations on Graphics Processing Units

Single precision (SP) arithmetic can be greatly accelerated as compared to double precision (DP) arithmetic on graphics processing units (GPUs). However, the use of SP in the whole process of electronic structure calculations is inappropriate for the required accuracy. We propose a 3-fold dynamic precision approach for accelerated calculations but still with the accuracy of DP. Here, SP, DP, and mixed precision are dynamically switched during an iterative diagonalization process. We applied this approach to the locally optimal block preconditioned conjugate gradient method to accelerate a large-scale eigenvalue solver for the Kohn-Sham equation. We determined a proper threshold for switching each precision scheme by examining the convergence pattern on the eigenvalue solver only with the kinetic energy operator of the Kohn-Sham Hamiltonian. As a result, we achieved up to 8.53× and 6.60× speedups for band structure and self-consistent field calculations, respectively, for test systems under various boundary conditions on NVIDIA GPUs.

Bayesian MRI reconstruction with joint uncertainty estimation using diffusion models

PURPOSE

We introduce a framework that enables efficient sampling from learned probability distributions for MRI reconstruction.

METHOD

Samples are drawn from the posterior distribution given the measured k-space using the Markov chain Monte Carlo (MCMC) method, different from conventional deep learning-based MRI reconstruction techniques. In addition to the maximum a posteriori estimate for the image, which can be obtained by maximizing the log-likelihood indirectly or directly, the minimum mean square error estimate and uncertainty maps can also be computed from those drawn samples. The data-driven Markov chains are constructed with the score-based generative model learned from a given image database and are independent of the forward operator that is used to model the k-space measurement.

RESULTS

We numerically investigate the framework from these perspectives: (1) the interpretation of the uncertainty of the image reconstructed from undersampled k-space; (2) the effect of the number of noise scales used to train the generative models; (3) using a burn-in phase in MCMC sampling to reduce computation; (4) the comparison to conventional ℓ 1 $$ {\ell}_1 $$ -wavelet regularized reconstruction; (5) the transferability of learned information; and (6) the comparison to fastMRI challenge.

CONCLUSION

A framework is described that connects the diffusion process and advanced generative models with Markov chains. We demonstrate its flexibility in terms of contrasts and sampling patterns using advanced generative priors and the benefits of also quantifying the uncertainty for every pixel.

An interpretive constrained linear model for ResNet and MgNet

We propose a constrained linear data-feature-mapping model as an interpretable mathematical model for image classification using a convolutional neural network (CNN). From this viewpoint, we establish detailed connections between the traditional iterative schemes for linear systems and the architectures of the basic blocks of ResNet- and MgNet-type models. Using these connections, we present some modified ResNet models that, compared with the original models, have fewer parameters but can produce more accurate results, thereby demonstrating the validity of this constrained learning data-feature-mapping assumption. Based on this assumption, we further propose a general data-feature iterative scheme to demonstrate the rationality of MgNet. We also provide a systematic numerical study on MgNet to show its success and advantages in image classification problems, particularly in comparison with established networks.

A Levenberg-Marquardt Method for Tensor Approximation

This paper presents a tensor approximation algorithm, based on the Levenberg–Marquardt method for the nonlinear least square problem, to decompose large-scale tensors into the sum of the products of vector groups of a given scale, or to obtain a low-rank tensor approximation without losing too much accuracy. An Armijo-like rule of inexact line search is also introduced into this algorithm. The result of the tensor decomposition is adjustable, which implies that the decomposition can be specified according to the users’ requirements. The convergence is proved, and numerical experiments show that it has some advantages over the classical Levenberg–Marquardt method. This algorithm is applicable to both symmetric and asymmetric tensors, and it is expected to play a role in the field of large-scale data compression storage and large-scale tensor approximation operations.

A Reinforcement Learning Framework to Discover Natural Flavor Molecules

Flavor is the focal point in the flavor industry, which follows social tendencies and behaviors. The research and development of new flavoring agents and molecules are essential in this field. However, the development of natural flavors plays a critical role in modern society. Considering this, the present work proposes a novel framework based on scientific machine learning to undertake an emerging problem in flavor engineering and industry. It proposes a combining system composed of generative and reinforcement learning models. Therefore, this work brings an innovative methodology to design new flavor molecules. The molecules were evaluated regarding synthetic accessibility, the number of atoms, and the likeness to a natural or pseudo-natural product. This work brings as contributions the implementation of a web scraper code to sample a flavors database and the integration of two scientific machine learning techniques in a complex system as a framework. The implementation of the complex system instead of the generative model by itself obtained 10% more molecules within the optimal results. The designed molecules obtained as an output of the reinforcement learning model’s generation were assessed regarding their existence or not in the market and whether they are already used in the flavor industry or not. Thus, we corroborated the potentiality of the framework presented for the search of molecules to be used in the development of flavor-based products.

Investigating the effects of microstructural changes induced by myocardial infarction on the elastic parameters of the heart

Within this work, we investigate how physiologically observed microstructural changes induced by myocardial infarction impact the elastic parameters of the heart. We use the LMRP model for poroelastic composites (Miller and Penta in Contin Mech Thermodyn 32:1533-1557, 2020) to describe the microstructure of the myocardium and investigate microstructural changes such as loss of myocyte volume and increased matrix fibrosis as well as increased myocyte volume fraction in the areas surrounding the infarct. We also consider a 3D framework to model the myocardium microstructure with the addition of the intercalated disks, which provide the connections between adjacent myocytes. The results of our simulations agree with the physiological observations that can be made post-infarction. That is, the infarcted heart is much stiffer than the healthy heart but with reperfusion of the tissue it begins to soften. We also observe that with the increase in myocyte volume of the non-damaged myocytes the myocardium also begins to soften. With a measurable stiffness parameter the results of our model simulations could predict the range of porosity (reperfusion) that could help return the heart to the healthy stiffness. It would also be possible to predict the volume of the myocytes in the area surrounding the infarct from the overall stiffness measurements.

Models and Algorithms for the Refinement of Therapeutic Approaches for Retinal Diseases

We are developing a Virtual Eye for in silico therapies to accelerate research and drug development. In this paper, we present a model for drug distribution in the vitreous body that enables personalized therapy in ophthalmology. The standard treatment for age-related macular degeneration is anti-vascular endothelial growth factor (VEGF) drugs administered by repeated injections. The treatment is risky, unpopular with patients, and some of them are unresponsive with no alternative treatment. Much attention is paid to the efficacy of these drugs, and many efforts are being made to improve them. We are designing a mathematical model and performing long-term three-dimensional Finite Element simulations for drug distribution in the human eye to gain new insights in the underlying processes using computational experiments. The underlying model consists of a time-dependent convection-diffusion equation for the drug coupled with a steady-state Darcy equation describing the flow of aqueous humor through the vitreous medium. The influence of collagen fibers in the vitreous on drug distribution is included by anisotropic diffusion and the gravity via an additional transport term. The resulting coupled model was solved in a decoupled way: first the Darcy equation with mixed finite elements, then the convection-diffusion equation with trilinear Lagrange elements. Krylov subspace methods are used to solve the resulting algebraic system. To cope with the large time steps resulting from the simulations over 30 days (operation time of 1 anti-VEGF injection), we apply the strong A-stable fractional step theta scheme. Using this strategy, we compute a good approximation to the solution that converges quadratically in both time and space. The developed simulations were used for the therapy optimization, for which specific output functionals are evaluated. We show that the effect of gravity on drug distribution is negligible, that the optimal pair of injection angles is (50∘,50∘), that larger angles can result in 38% less drug at the macula, and that in the best case only 40% of the drug reaches the macula while the rest escapes, e.g., through the retina, that by using heavier drug molecules, more of the drug concentration reaches the macula in an average of 30 days. As a refined therapy, we have found that for longer-acting drugs, the injection should be made in the center of the vitreous, and for more intensive initial treatment, the drug should be injected even closer to the macula. In this way, we can perform accurate and efficient treatment testing, calculate the optimal injection position, perform drug comparison, and quantify the effectiveness of the therapy using the developed functionals. We describe the first steps towards virtual exploration and improvement of therapy for retinal diseases such as age-related macular degeneration.

Stopping-power ratio estimation for proton radiotherapy using dual-energy computed tomography and prior-image constrained denoising

BACKGROUND

Dual-energy computed tomography (DECT) is a promising technique for estimating stopping-power ratio (SPR) for proton therapy planning. It is known, however, that deriving electron density (ED) and effective atomic number (EAN) from DECT data can cause noise amplification in the resulting SPR images. This can negate the benefits of DECT.

PURPOSE

This work introduces a new algorithm for estimating SPR from DECT with noise suppression, using a pair of CT scans with spectral separation. The method is demonstrated using phantom measurements.

MATERIALS AND METHODS

An iterative algorithm is presented, reconstructing ED and EAN with noise suppression, based on Prior Image Constrained Denoising (PIC-D). The algorithm is tested using a Siemens Definition AS+ CT scanner (Siemens Healthcare, Forchheim, Germany). Three phantoms are investigated: a calibration phantom (CIRS 062M), a QA phantom (CATPHAN 700), and an anthropomorphic head phantom (CIRS 731-HN). A task-transfer function (TTF) and the noise power spectrum are derived from SPR images of the QA phantom for the evaluation of image quality. Comparisons of accuracy and noise for ED, EAN, and SPR are made for various versions of the algorithm in comparison to a solution based on Siemens syngo.via Rho/Z software and the current clinical standard of a single-energy CT stoichiometric calibration. A gamma analysis is also applied to the SPR images of the head phantom and water-equivalent distance (WED) is evaluated in a treatment planning system for a proton treatment field.

RESULTS

The algorithm is effective at suppressing noise in both ED and EAN and hence also SPR. The noise is tunable to a level equivalent to or lower than that of the syngo.via Rho/Z software. The spatial resolution (10% and 50% frequencies in the TTF) does not degrade even for the highest noise suppression investigated, although the average spatial frequency of noise does decrease. The PIC-D algorithm showed better accuracy than syngo.via Rho/Z for low density materials. In the calibration phantom, it was superior even when excluding lung substitutes, with root-mean-square deviations for ED and EAN less than 0.3% and 2%, respectively, compared to 0.5% and 3%. In the head phantom, however, the SPR accuracy of the PIC-D algorithm was comparable (excluding sinus tissue) to that derived from syngo.via Rho/Z: less than 1% error for soft tissue, brain, and trabecular bone substitutes and 5-7% for cortical bone, with the larger error for the latter likely related to the phantom geometry. Gamma evaluation showed that PIC-D can suppress noise in a patient-like geometry without introducing substantial errors in SPR. The absolute pass rates were almost identical for PIC-D and syngo.via Rho/Z. In the WED evaluations no general differences were shown.

CONCLUSIONS

The PIC-D DECT algorithm provides scanner-specific calibration and tunable noise suppression. It is vendor agnostic and applicable to any pair of CT scans with spectral separation. Improved accuracy to current methods was not clearly demonstrated for the complex geometry of a head phantom, but the suppression of noise without spatial resolution degradation and the possibility of incorporating constraints on image properties, suggests the usefulness of the approach.

Mixed multiscale BM4D for three-dimensional optical coherence tomography denoising

A multiscale extension for the well-known block matching and 4D filtering (BM4D) method is proposed by analyzing and extending the wavelet subbands denoising method in such a way that the proposed method avoids directly denoising detail subbands, which considerably simplifies the computations and makes the multiscale processing feasible in 3D. To this end, we first derive the multiscale construction method in 2D and propose multiscale extensions for three 2D natural image denoising methods. Then, the derivation is extended to 3D by proposing mixed multiscale BM4D (mmBM4D) for optical coherence tomography (OCT) image denoising. We tested mmBM4D on three public OCT datasets captured by various imaging devices. The experiments revealed that mmBM4D significantly outperforms its original counterpart and performs on par with the state-of-the-art OCT denoising methods. In terms of peak-signal-to-noise-ratio (PSNR), mmBM4D surpasses the original BM4D by more than 0.68 decibels over the first dataset. In the second and third datasets, significant improvements in the mean to standard deviation ratio, contrast to noise ratio, and equivalent number of looks were achieved. Furthermore, on the downstream task of retinal layer segmentation, the layer quality preservation of the compared OCT denoising methods is evaluated.

A Computational Study of Dynamic Obstruction in Type B Aortic Dissection

A serious complication in aortic dissection is dynamic obstruction of the true lumen (TL). Dynamic obstruction results in malperfusion, a blockage of blood flow to a vital organ. Clinical data reveal that increases in central blood pressure promote dynamic obstruction. However, the mechanisms by which high pressures result in TL collapse are underexplored and poorly understood. Here, we developed a computational model to investigate biomechanical and hemodynamical factors involved in Dynamic obstruction. We hypothesize that relatively small pressure gradient between TL and false lumen (FL) are sufficient to displace the flap and induce obstruction. An idealized fluid-structure interaction model of type B aortic dissection was created. Simulations were performed under mean cardiac output while inducing dynamic changes in blood pressure by altering FL outflow resistance. As FL resistance increased, central aortic pressure increased from 95.7 to 115.3 mmHg. Concurrent with blood pressure increase, flap motion was observed, resulting in TL collapse, consistent with clinical findings. The maximum pressure gradient between TL and FL over the course of the dynamic obstruction was 4.5 mmHg, consistent with our hypothesis. Furthermore, the final stage of dynamic obstruction was very sudden in nature, occurring over a short time (<1 s) in our simulation, consistent with the clinical understanding of this dramatic event. Simulations also revealed sudden drops in flow and pressure in the TL in response to the flap motion, consistent with first stages of malperfusion. To our knowledge, this study represents the first computational analysis of potential mechanisms driving dynamic obstruction in aortic dissection.

Model-free forecasting of partially observable spatiotemporally chaotic systems

Reservoir computing is a powerful tool for forecasting turbulence because its simple architecture has the computational efficiency to handle high-dimensional systems. Its implementation, however, often requires full state-vector measurements and knowledge of the system nonlinearities. We use nonlinear projector functions to expand the system measurements to a high dimensional space and then feed them to a reservoir to obtain forecasts. We demonstrate the application of such reservoir computing networks on spatiotemporally chaotic systems, which model several features of turbulence. We show that using radial basis functions as nonlinear projectors enables complex system nonlinearities to be captured robustly even with only partial observations and without knowing the governing equations. Finally, we show that when measurements are sparse or incomplete and noisy, such that even the governing equations become inaccurate, our networks can still produce reasonably accurate forecasts, thus paving the way towards model-free forecasting of practical turbulent systems.

Data-driven flow-map models for data-efficient discovery of dynamics and fast uncertainty quantification of biological and biochemical systems

Computational models are increasingly used to investigate and predict the complex dynamics of biological and biochemical systems. Nevertheless, governing equations of a biochemical system may not be (fully) known, which would necessitate learning the system dynamics directly from, often limited and noisy, observed data. On the other hand, when expensive models are available, systematic and efficient quantification of the effects of model uncertainties on quantities of interest can be an arduous task. This paper leverages the notion of flow-map (de)compositions to present a framework that can address both of these challenges via learning data-driven models useful for capturing the dynamical behavior of biochemical systems. Data-driven flow-map models seek to directly learn the integration operators of the governing differential equations in a black-box manner, irrespective of structure of the underlying equations. As such, they can serve as a flexible approach for deriving fast-to-evaluate surrogates for expensive computational models of system dynamics, or, alternatively, for reconstructing the long-term system dynamics via experimental observations. We present a data-efficient approach to data-driven flow-map modeling based on polynomial chaos Kriging. The approach is demonstrated for discovery of the dynamics of various benchmark systems and a coculture bioreactor subject to external forcing, as well as for uncertainty quantification of a microbial electrosynthesis reactor. Such data-driven models and analyses of dynamical systems can be paramount in the design and optimization of bioprocesses and integrated biomanufacturing systems.

Fast simultaneous estimation of nD transport coefficients and source function in perturbation experiments

In the calculation of transport coefficients from experimental data precise knowledge of the source is usually assumed, while the identification of the coefficients focuses on specific geometries and one spatial variable. This paper presents a method for the simultaneous estimation of both the distributions of transport coefficients as well as the source profile. A convex solution of the inverse problem is retained which makes the calculations highly computational efficient. Moreover, this allows for the estimation of multi-dimensional transport coefficients, source terms, and in the future the analysis of the effect of regularization on experimental data and transport coefficient distributions.

Local Hydration Control and Functional Implications Through S-Nitrosylation of Proteins: Kirsten Rat Sarcoma Virus (K-RAS) and Hemoglobin (Hb)

S-nitrosylation, the covalent addition of NO to the thiol side chain of cysteine, is an important post-transitional modification (PTM) that can affect the function of proteins. As such, PTMs extend and diversify protein function and thus characterizing consequences of PTM at a molecular level is of great interest. Although PTMs can be detected through various direct/indirect methods, they lack the capability to investigate the modifications with molecular detail. In the present work local and global structural dynamics, their correlation, the hydration structure, and the infrared spectroscopy for WT and S-nitrosylated Kirsten rat sarcoma virus (K-RAS) and hemoglobin (Hb) are characterized from molecular dynamics simulations. It is found that attaching NO to Cys118 in K-RAS rigidifies the protein in the Switch-I region which has functional implications, whereas for Hb, nitrosylation at Cys93 at the β₁ chain increases the flexibility of secondary structural motives for Hb in its T₀ and R₄ conformational substates. Solvent water access decreased by 40% after nitrosylation in K-RAS, similar to Hb for which, however, local hydration of the R₄SNO state is yet lower than for T₀SNO. Finally, S-nitrosylation leads to detectable peaks for the NO stretch frequency, but the congested IR spectral region will make experimental detection of these bands difficult. Overall, S-nitrosylation in these two proteins is found to influence hydration, protein flexibility, and conformational dynamics which are all eventually involved in protein regulation and function at a molecular level.

Prevalence estimation and optimal classification methods to account for time dependence in antibody levels

Serology testing can identify past infection by quantifying the immune response of an infected individual providing important public health guidance. Individual immune responses are time-dependent, which is reflected in antibody measurements. Moreover, the probability of obtaining a particular measurement from a random sample changes due to changing prevalence (i.e., seroprevalence, or fraction of individuals exhibiting an immune response) of the disease in the population. Taking into account these personal and population-level effects, we develop a mathematical model that suggests a natural adaptive scheme for estimating prevalence as a function of time. We then combine the estimated prevalence with optimal decision theory to develop a time-dependent probabilistic classification scheme that minimizes the error associated with classifying a value as positive (history of infection) or negative (no such history) on a given day since the start of the pandemic. We validate this analysis by using a combination of real-world and synthetic SARS-CoV-2 data and discuss the type of longitudinal studies needed to execute this scheme in real-world settings.

Rheology of Pseudomonas fluorescens biofilms: From experiments to predictive DPD mesoscopic modeling

Bacterial biofilms mechanically behave as viscoelastic media consisting of micron-sized bacteria cross-linked to a self-produced network of extracellular polymeric substances (EPSs) embedded in water. Structural principles for numerical modeling aim at describing mesoscopic viscoelasticity without losing details on the underlying interactions existing in wide regimes of deformation under hydrodynamic stress. Here, we approach the computational challenge to model bacterial biofilms for predictive mechanics in silico under variable stress conditions. Up-to-date models are not entirely satisfactory due to the plethora of parameters required to make them functioning under the effects of stress. As guided by the structural depiction gained in a previous work with Pseudomonas fluorescens [Jara et al., Front. Microbiol. 11, 588884 (2021)], we propose a mechanical modeling by means of Dissipative Particle Dynamics (DPD), which captures the essentials of topological and compositional interactions between bacterial particles and cross-linked EPS-embedding under imposed shear. The P. fluorescens biofilms have been modeled under mechanical stress mimicking shear stresses as undergone in vitro. The predictive capacity for mechanical features in DPD-simulated biofilms has been investigated by varying the externally imposed field of shear strain at variable amplitude and frequency. The parametric map of essential biofilm ingredients has been explored by making the rheological responses to emerge among conservative mesoscopic interactions and frictional dissipation in the underlying microscale. The proposed coarse grained DPD simulation qualitatively catches the rheology of the P. fluorescens biofilm over several decades of dynamic scaling.

Optimal classification and generalized prevalence estimates for diagnostic settings with more than two classes

An accurate multiclass classification strategy is crucial to interpreting antibody tests. However, traditional methods based on confidence intervals or receiver operating characteristics lack clear extensions to settings with more than two classes. We address this problem by developing a multiclass classification based on probabilistic modeling and optimal decision theory that minimizes the convex combination of false classification rates. The classification process is challenging when the relative fraction of the population in each class, or generalized prevalence, is unknown. Thus, we also develop a method for estimating the generalized prevalence of test data that is independent of classification of the test data. We validate our approach on serological data with severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) naïve, previously infected, and vaccinated classes. Synthetic data are used to demonstrate that (i) prevalence estimates are unbiased and converge to true values and (ii) our procedure applies to arbitrary measurement dimensions. In contrast to the binary problem, the multiclass setting offers wide-reaching utility as the most general framework and provides new insight into prevalence estimation best practices.

Efficient forecasting and uncertainty quantification for large-scale account level Monte Carlo models of debt recovery

The state-of-the-art in forecasting debt recovery from portfolios of non-performing unsecured consumer loans is to use stochastic models of payment behaviour of individual customers. Monte Carlo simulation of these models can enable forecasting of collections, where computational complexity arises from the very large number of heterogeneous accounts. We aim to solve 2 problems: efficient allocation of computational resources and quantification of uncertainty. We show that robust estimators of population-level variance can be constructed using unbiased estimators of the variance of individual accounts. The proposed methods are demonstrated through application to a model similar to those used in practice.

A physics-informed neural network based on mixed data sampling for solving modified diffusion equations

We developed a physics-informed neural network based on a mixture of Cartesian grid sampling and Latin hypercube sampling to solve forward and backward modified diffusion equations. We optimized the parameters in the neural networks and the mixed data sampling by considering the squeeze boundary condition and the mixture coefficient, respectively. Then, we used a given modified diffusion equation as an example to demonstrate the efficiency of the neural network solver for forward and backward problems. The neural network results were compared with the numerical solutions, and good agreement with high accuracy was observed. This neural network solver can be generalized to other partial differential equations.

Neural network potentials for chemistry: concepts, applications and prospects

Artificial Neural Networks (NN) are already heavily involved in methods and applications for frequent tasks in the field of computational chemistry such as representation of potential energy surfaces (PES) and spectroscopic predictions. This perspective provides an overview of the foundations of neural network-based full-dimensional potential energy surfaces, their architectures, underlying concepts, their representation and applications to chemical systems. Methods for data generation and training procedures for PES construction are discussed and means for error assessment and refinement through transfer learning are presented. A selection of recent results illustrates the latest improvements regarding accuracy of PES representations and system size limitations in dynamics simulations, but also NN application enabling direct prediction of physical results without dynamics simulations. The aim is to provide an overview for the current state-of-the-art NN approaches in computational chemistry and also to point out the current challenges in enhancing reliability and applicability of NN methods on a larger scale.

A spectral method for assessing and combining multiple data visualizations

Dimension reduction is an indispensable part of modern data science, and many algorithms have been developed. However, different algorithms have their own strengths and weaknesses, making it important to evaluate their relative performance, and to leverage and combine their individual strengths. This paper proposes a spectral method for assessing and combining multiple visualizations of a given dataset produced by diverse algorithms. The proposed method provides a quantitative measure - the visualization eigenscore - of the relative performance of the visualizations for preserving the structure around each data point. It also generates a consensus visualization, having improved quality over individual visualizations in capturing the underlying structure. Our approach is flexible and works as a wrapper around any visualizations. We analyze multiple real-world datasets to demonstrate the effectiveness of the method. We also provide theoretical justifications based on a general statistical framework, yielding several fundamental principles along with practical guidance.

A scalable thin-film defect quantify model under imbalanced regression and classification task based on computer vision

Optical coating damage detection is a part of both industrial production and scientific research. Traditional methods require sophisticated expert systems or experienced front-line producers, and the cost of these methods rises dramatically when film types or inspection environments change. In practice, it has been found that customized expert systems imply a significant investment of time and money, and we expect to find a method that can perform this task automatically and quickly, while at the same time the method should be adaptable to the later addition of coating types and the ability to identify damage kinds. In this paper, we propose a deep neural network-based detection tool that splits the task into two parts: damage classification and damage degree regression. Introduces attention mechanisms and Embedding operations to enhance the performance of the model. It was found that the damage type detection accuracy of our model reached 93.65%, and the regression loss was kept within 10% on different data sets. We believe that deep neural networks have great potential to tackle industrial defect detection by significantly reducing the design cost and time of traditional expert systems, while gaining the ability to detect entirely new damage types at a fraction of the cost.

SDEGen: learning to evolve molecular conformations from thermodynamic noise for conformation generation

Generation of representative conformations for small molecules is a fundamental task in cheminformatics and computer-aided drug discovery, but capturing the complex distribution of conformations that contains multiple low energy minima is still a great challenge. Deep generative modeling, aiming to learn complex data distributions, is a promising approach to tackle the conformation generation problem. Here, inspired by stochastic dynamics and recent advances in generative modeling, we developed SDEGen, a novel conformation generation model based on stochastic differential equations. Compared with existing conformation generation methods, it enjoys the following advantages: (1) high model capacity to capture multimodal conformation distribution, thereby searching for multiple low-energy conformations of a molecule quickly, (2) higher conformation generation efficiency, almost ten times faster than the state-of-the-art score-based model, ConfGF, and (3) a clear physical interpretation to learn how a molecule evolves in a stochastic dynamics system starting from noise and eventually relaxing to the conformation that falls in low energy minima. Extensive experiments demonstrate that SDEGen has surpassed existing methods in different tasks for conformation generation, interatomic distance distribution prediction, and thermodynamic property estimation, showing great potential for real-world applications.

Simulating structured fluids with tensorial viscoelasticity

We consider an immersed elastic body that is actively driven through a structured fluid by a motor or an external force. The behavior of such a system generally cannot be solved analytically, necessitating the use of numerical methods. However, current numerical methods omit important details of the microscopic structure and dynamics of the fluid, which can modulate the magnitudes and directions of viscoelastic restoring forces. To address this issue, we develop a simulation platform for modeling viscoelastic media with tensorial elasticity. We build on the lattice Boltzmann algorithm and incorporate viscoelastic forces, elastic immersed objects, a microscopic orientation field, and coupling between viscoelasticity and the orientation field. We demonstrate our method by characterizing how the viscoelastic restoring force on a driven immersed object depends on various key parameters as well as the tensorial character of the elastic response. We find that the restoring force depends non-monotonically on the rate of diffusion of the stress and the size of the object. We further show how the restoring force depends on the relative orientation of the microscopic structure and the pulling direction. These results imply that accounting for previously neglected physical features, such as stress diffusion and the microscopic orientation field, can improve the realism of viscoelastic simulations. We discuss possible applications and extensions to the method.

The prediction of contact force networks in granular materials based on graph neural networks

The contact force network, usually organized inhomogeneously by the inter-particle forces on the bases of the contact network topologies, is essential to the rigidity and stability in amorphous solids. How to capture such a "backbone" is crucial to the understanding of various anomalous properties or behaviors in those materials, which remains a central challenge presently in physics, engineering, or material science. Here, we use a novel graph neural network to predict the contact force network in two-dimensional granular materials under uniaxial compression. With the edge classification model in the framework of the deep graph library, we show that the inter-particle contact forces can be accurately estimated purely from the knowledge of the static microstructures, which can be acquired from a discrete element method or directly visualized from experimental methods. By testing the granular packings with different structural disorders and pressure, we further demonstrate the robustness of the optimized graph neural network to changes in various model parameters. Our research tries to provide a new way of extracting the information about the inter-particle forces, which substantially improves the efficiency and reduces the costs compared to the traditional experiments.

Modelling of thrombus formation using smoothed particle hydrodynamics method

In this paper a novel model, based on the smoothed particle hydrodynamics (SPH) method, is proposed to simulate thrombus formation. This describes the main phases of the coagulative cascade through the balance of four biochemical species and three type of platelets. SPH particles can switch from fluid to solid phase when specific biochemical and physical conditions are satisfied. The interaction between blood and the forming blood clot is easily handled by an innovative monolithic FSI approach. Fluid-solid coupling is modelled by introducing elastic binds between solid particles, without requiring detention and management of the interface between the two media. The proposed model is able to realistically reproduce the thromboembolic process, as confirmed by the comparison of numerical results with experimental data available in the literature.

Segmentation-based tracking of macrophages in 2D＋time microscopy movies inside a living animal

The automated segmentation and tracking of macrophages during their migration are challenging tasks due to their dynamically changing shapes and motions. This paper proposes a new algorithm to achieve automatic cell tracking in time-lapse microscopy macrophage data. First, we design a segmentation method employing space-time filtering, local Otsu's thresholding, and the SUBSURF (subjective surface segmentation) method. Next, the partial trajectories for cells overlapping in the temporal direction are extracted in the segmented images. Finally, the extracted trajectories are linked by considering their direction of movement. The segmented images and the obtained trajectories from the proposed method are compared with those of the semi-automatic segmentation and manual tracking. The proposed tracking achieved 97.4% of accuracy for macrophage data under challenging situations, feeble fluorescent intensity, irregular shapes, and motion of macrophages. We expect that the automatically extracted trajectories of macrophages can provide pieces of evidence of how macrophages migrate depending on their polarization modes in the situation, such as during wound healing.

Molecular dynamics simulation of thermal characteristics of globulin protein dissolved in dilute salt solutions using equilibrium and non-equilibrium methods

The aggregation of 7S globulin protein (7SGP) in mature soybean (Glycine max) seeds is an extracellular matrix protein. This atomic compound can be detected in various food products. So, this protein structure's thermal properties (TP) can be important for various food industry products. Molecular Dynamics (MD) simulations describe the atomic arrangement of this protein and forecast TP of them in various initial conditions. The present computational work estimates the 7SGP thermal behavior (TB) by equilibrium (E) and non-equilibrium (NE) methods. In these two methods, the 7SGP is represented using DREIDING interatomic potential. MD outputs predicted 0.59 and 0.58 W/mK values for thermal conductivity (TC) of 7SGP at T₀ = 300 K and P₀ = 1 bar using E and NE methods. Furthermore, computational results represented that the pressure (P) and temperature (T) are significant factors for the TB of 7SGP. Numerically, TC of 7SGP reaches 0.68 W/mK, 0.52 W/mK by T/P increasing. MD results predicted the interaction energy (IE) between 7SGP and aqueous media could fluctuate between -110.64 and 161.53 kcal/mol by the change in T/P after t = 10 ns?These results should be supposed to design new methods for various food industry purposes, such as producing and processing edible oils.

Fluid structure interaction analysis to stratify the behavior of different atheromatous carotid plaques

BACKGROUND

In asymptomatic carotid stenosis (ACS), different plaque types, i.e. lipidic (LP), fibrous (FP), and calcific (CP), could have different hemodynamic and structural behaviors.

METHODS

Different carotid plaques, reconstructed from medical imaging of ACS >70%, were analyzed by computing fluid structure interaction (FSI), modeling the spatial distribution of wall shear stresses (WSS), plaque displacements (D), von Mises stresses (VMS), and absorbed elastic energy (AEE) together with their maximum-in-space values at the systole (WSS<inf>syst</inf>, D<inf>syst</inf>, VMS<inf>syst</inf> and AEE<inf>syst</inf>).

RESULTS

WSS resulted significantly higher in CP, whereas D and VMS showed the highest values for LP. Regarding AEE<inf>syst</inf> stored by the plaques, LP absorbed in average 2320 J/m³, FP 408 J/m³ (470%) and CP 99 J/m³ (2240%), (P<0.01, P<0.01, and P<0.01, respectively).

CONCLUSIONS

Depending upon their nature, plaques store different deformations and inner distributions of forces, thus potentially influencing their vulnerability.