Verification method of Monte Carlo codes for transport processes with arbitrary accuracy

Integrating core physics and machine learning for improved parameter prediction in boiling water reactor operations

This study introduces a novel method for enhancing Boiling Water Reactor (BWR) operation simulations by integrating machine learning (ML) models with conventional simulation techniques. The ML model is trained to identify and correct errors in low-fidelity simulation outputs, traditionally derived from core physics computations. These corrections aim to align the low-fidelity results closely with high-fidelity data. Precise predictions of nuclear reactor parameters like core eigenvalue and power distribution are crucial for efficient fuel management and adherence to technical specifications. Current high-fidelity transport calculations, while accurate, are impractical for real-time predictions due to extensive computational demands. Our approach, therefore, utilizes the standard two-step simulation process-assembly-level lattice physics calculations followed by whole-core nodal diffusion computations-to generate initial results, which are then refined using the ML-based error correction model. The methodology focuses on improving simulation accuracy in regular BWR operations rather than developing a universal ML predictor for reactor physics. By training an advanced neural network model on the difference in high-fidelity and low-fidelity simulations, the model can reduce the nodal power error from low-fidelity simulations to around 1% on average and the core eigenvalue down to under 100 pcm. This result is under the condition of the normal variations of control rod pattern and core flow rate changes in standard BWR operations used in the training and evaluation of the machine learning model. This work suggests a promising approach for achieving more accurate, computationally feasible simulation solutions in nuclear reactor operation and management.

Q-Factor Optimization of Modes in Ordered and Disordered Photonic Systems Using Non-Hermitian Perturbation Theory

The quality factor, Q, of photonic resonators permeates most figures of merit in applications that rely on cavity-enhanced light-matter interaction such as all-optical information processing, high-resolution sensing, or ultralow-threshold lasing. As a consequence, large-scale efforts have been devoted to understanding and efficiently computing and optimizing the Q of optical resonators in the design stage. This has generated large know-how on the relation between physical quantities of the cavity, e.g., Q, and controllable parameters, e.g., hole positions, for engineered cavities in gaped photonic crystals. However, such a correspondence is much less intuitive in the case of modes in disordered photonic media, e.g., Anderson-localized modes. Here, we demonstrate that the theoretical framework of quasinormal modes (QNMs), a non-Hermitian perturbation theory for shifting material boundaries, and a finite-element complex eigensolver provide an ideal toolbox for the automated shape optimization of Q of a single photonic mode in both ordered and disordered environments. We benchmark the non-Hermitian perturbation formula and employ it to optimize the Q-factor of a photonic mode relative to the position of vertically etched holes in a dielectric slab for two different settings: first, for the fundamental mode of L3 cavities with various footprints, demonstrating that the approach simultaneously takes in-plane and out-of-plane losses into account and leads to minor modal structure modifications; and second, for an Anderson-localized mode with an initial Q of 200, which evolves into a completely different mode, displaying a threefold reduction in the mode volume, a different overall spatial location, and, notably, a 3 order of magnitude increase in Q.

Fluence rate directly derived from photon pathlengths: a tool for Monte Carlo simulations in biomedical optics

In biomedical optics, the mean fluence rate of photons, assessed in a sub-volume of a propagating medium, is classically obtained in Monte Carlo simulations by taking into account the power deposited by the absorbed photons in the sub-volume. In the present contribution, we propose and analytically demonstrate an alternative method based on the assessment of the mean pathlength traveled by all the photons inside the sub-volume. Few practical examples of its applications are given. This method has the advantage of improving, in many cases, the statistics and the convergence of the Monte Carlo simulations. Further, it also works when the absorption coefficient is nil and for a non-constant spatial distribution of the absorption coefficient inside the sub-volume. The proposed approach is a re-visitation of a well-known method applied in radiation and nuclear physics in the context of radiative transfer, where it can be derived in a more natural manner.

On the mean path length invariance property for random walks of animals in open environment

Random walks are common in nature and are at the basis of many different phenomena that span from neutrons and light scattering to the behaviour of animals. Despite the evident differences among all these phenomena, theory predicts that they all share a common fascinating feature known as Invariance Property (IP). In a nutshell, IP means that the mean length of the total path of a random walker inside a closed domain is fixed by the geometry and size of the medium. Such a property has been demonstrated to hold not only in optics, but recently also in the field of biology, by studying the movement of bacteria. However, the range of validity of such a universal property, strictly linked to the fulfilment of equilibrium conditions and to the statistical distributions of the steps of the random walkers, is not trivial and needs to be studied in different contexts, such as in the case of biological entities occupied in random foraging in an open environment. Hence, in this paper the IP in a virtual medium inside an open environment has been studied by using actual movements of animals recorded in nature. In particular, we analysed the behaviour of a grazer mollusc, the chiton Acanthopleura granulata. The results depart from those predicted by the IP when the dimension of the medium increases. Such findings are framed in both the condition of nonequilibrium of the walkers, which is typical of animals in nature, and the characteristics of actual animal movements.

Efficient computation of the steady-state and time-domain solutions of the photon diffusion equation in layered turbid media

Accurate and efficient forward models of photon migration in heterogeneous geometries are important for many applications of light in medicine because many biological tissues exhibit a layered structure of independent optical properties and thickness. However, closed form analytical solutions are not readily available for layered tissue-models, and often are modeled using computationally expensive numerical techniques or theoretical approximations that limit accuracy and real-time analysis. Here, we develop an open-source accurate, efficient, and stable numerical routine to solve the diffusion equation in the steady-state and time-domain for a layered cylinder tissue model with an arbitrary number of layers and specified thickness and optical coefficients. We show that the steady-state ([Formula: see text] ms) and time-domain ([Formula: see text] ms) fluence (for an 8-layer medium) can be calculated with absolute numerical errors approaching machine precision. The numerical implementation increased computation speed by 3 to 4 orders of magnitude compared to previously reported theoretical solutions in layered media. We verify our solutions asymptotically to homogeneous tissue geometries using closed form analytical solutions to assess convergence and numerical accuracy. Approximate solutions to compute the reflected intensity are presented which can decrease the computation time by an additional 2-3 orders of magnitude. We also compare our solutions for 2, 3, and 5 layered media to gold-standard Monte Carlo simulations in layered tissue models of high interest in biomedical optics (e.g. skin/fat/muscle and brain). The presented routine could enable more robust real-time data analysis tools in heterogeneous tissues that are important in many clinical applications such as functional brain imaging and diffuse optical spectroscopy.

Experimental imaging and Monte Carlo modeling of ultrafast pulse propagation in thin scattering slabs

SIGNIFICANCE

Most radiative transport problems in turbid media are typically associated with mm or cm scales, leading to typical time scales in the range of hundreds of ps or more. In certain cases, however, much thinner layers can also be relevant, which can dramatically alter the overall transport properties of a scattering medium. Studying scattering in these thin layers requires ultrafast detection techniques and adaptations to the common Monte Carlo (MC) approach.

AIM

We aim to discuss a few relevant aspects for the simulation of light transport in thin scattering membranes, and compare the obtained numerical results with experimental measurements based on an all-optical gating technique.

APPROACH

A thin membrane with controlled scattering properties based on polymer-dispersed TiO2 nanoparticles is fabricated for experimental validation. Transmittance measurements are compared against a custom open-source MC implementation including specific pulse profiles for tightly focused femtosecond laser pulses.

RESULTS

Experimental transmittance data of ultrafast pulses through a thin scattering sample are compared with MC simulations in the spatiotemporal domain to retrieve its scattering properties. The results show good agreement also at short distances and time scales.

CONCLUSIONS

When simulating light transport in scattering membranes with thicknesses in the orders of tens of micrometer, care has to be taken when describing the temporal, spatial, and divergence profiles of the source term, as well as the possible truncation of step length distributions, which could be introduced by simple strategies for the generation of random exponentially distributed variables.

Monte Carlo simulations in anomalous radiative transfer: tutorial

Anomalous radiative transfer (ART) theory represents a generalization of classical radiative transfer theory. The present tutorial aims to show how Monte Carlo (MC) codes describing the transport of photons in anomalous media can be implemented. We show that the heart of the method involves suitably describing, in a "non-classical" manner, photon steps starting from fixed light sources or from boundaries separating regions of the medium with different optical properties. To give a better sense of the importance of these particular photon step lengths, we also show numerically that the described approach is essential in preserving the invariance property for light propagation. An interesting byproduct of the MC method for ART is that it allows us to simplify the structure of "classical" MC codes, utilized, for example, in biomedical optics.

Two-step verification method for Monte Carlo codes in biomedical optics applications

SIGNIFICANCE

Code verification is an unavoidable step prior to using a Monte Carlo (MC) code. Indeed, in biomedical optics, a widespread verification procedure for MC codes is still missing. Analytical benchmarks that can be easily used for the verification of different MC routines offer an important resource.

AIM

We aim to provide a two-step verification procedure for MC codes enabling the two main tasks of an MC simulator: (1) the generation of photons' trajectories and (2) the intersections of trajectories with boundaries separating the regions with different optical properties. The proposed method is purely based on elementary analytical benchmarks, therefore, the correctness of an MC code can be assessed with a one-sample t-test.

APPROACH

The two-step verification is based on the following two analytical benchmarks: (1) the exact analytical formulas for the statistical moments of the spatial coordinates where the scattering events occur in an infinite medium and (2) the exact invariant solutions of the radiative transfer equation for radiance, fluence rate, and mean path length in media subjected to a Lambertian illumination.

RESULTS

We carried out a wide set of comparisons between MC results and the two analytical benchmarks for a wide range of optical properties (from non-scattering to highly scattering media, with different types of scattering functions) in an infinite non-absorbing medium (step 1) and in a non-absorbing slab (step 2). The deviations between MC results and exact analytical values are usually within two standard errors (i.e., t-tests not rejected at a 5% level of significance). The comparisons show that the accuracy of the verification increases with the number of simulated trajectories so that, in principle, an arbitrary accuracy can be obtained.

CONCLUSIONS

Given the simplicity of the verification method proposed, we envision that it can be widely used in the field of biomedical optics.