Empirical Classification of Trajectory Data: An Opportunity for the Use of Machine Learning in Molecular Dynamics

Hamiltonian Computational Chemistry: Geometrical Structures in Chemical Dynamics and Kinetics

The common geometrical (symplectic) structures of classical mechanics, quantum mechanics, and classical thermodynamics are unveiled with three pictures. These cardinal theories, mainly at the non-relativistic approximation, are the cornerstones for studying chemical dynamics and chemical kinetics. Working in extended phase spaces, we show that the physical states of integrable dynamical systems are depicted by Lagrangian submanifolds embedded in phase space. Observable quantities are calculated by properly transforming the extended phase space onto a reduced space, and trajectories are integrated by solving Hamilton's equations of motion. After defining a Riemannian metric, we can also estimate the length between two states. Local constants of motion are investigated by integrating Jacobi fields and solving the variational linear equations. Diagonalizing the symplectic fundamental matrix, eigenvalues equal to one reveal the number of constants of motion. For conservative systems, geometrical quantum mechanics has proved that solving the Schrödinger equation in extended Hilbert space, which incorporates the quantum phase, is equivalent to solving Hamilton's equations in the projective Hilbert space. In classical thermodynamics, we take entropy and energy as canonical variables to construct the extended phase space and to represent the Lagrangian submanifold. Hamilton's and variational equations are written and solved in the same fashion as in classical mechanics. Solvers based on high-order finite differences for numerically solving Hamilton's, variational, and Schrödinger equations are described. Employing the Hénon-Heiles two-dimensional nonlinear model, representative results for time-dependent, quantum, and dissipative macroscopic systems are shown to illustrate concepts and methods. High-order finite-difference algorithms, despite their accuracy in low-dimensional systems, require substantial computer resources when they are applied to systems with many degrees of freedom, such as polyatomic molecules. We discuss recent research progress in employing Hamiltonian neural networks for solving Hamilton's equations. It turns out that Hamiltonian geometry, shared with all physical theories, yields the necessary and sufficient conditions for the mutual assistance of humans and machines in deep-learning processes.

Learning effective dynamics from data-driven stochastic systems

Multiscale stochastic dynamical systems have been widely adopted to a variety of scientific and engineering problems due to their capability of depicting complex phenomena in many real-world applications. This work is devoted to investigating the effective dynamics for slow-fast stochastic dynamical systems. Given observation data on a short-term period satisfying some unknown slow-fast stochastic systems, we propose a novel algorithm, including a neural network called Auto-SDE, to learn an invariant slow manifold. Our approach captures the evolutionary nature of a series of time-dependent autoencoder neural networks with the loss constructed from a discretized stochastic differential equation. Our algorithm is also validated to be accurate, stable, and effective through numerical experiments under various evaluation metrics.

A neural network-assisted open boundary molecular dynamics simulation method

A neural network-assisted molecular dynamics method is developed to reduce the computational cost of open boundary simulations. Particle influxes and neural network-derived forces are applied at the boundaries of an open domain consisting of explicitly modeled Lennard-Jones atoms in order to represent the effects of the unmodeled surrounding fluid. Canonical ensemble simulations with periodic boundaries are used to train the neural network and to sample boundary fluxes. The method, as implemented in the LAMMPS, yields temperature, kinetic energy, potential energy, and pressure values within 2.5% of those calculated using periodic molecular dynamics and runs two orders of magnitude faster than a comparable grand canonical molecular dynamics system.

Machine learning classification of disrotatory IRC and conrotatory non-IRC trajectory motion for cyclopropyl radical ring opening

Quasiclassical trajectory analysis is now a standard tool to analyze non-minimum energy pathway motion of organic reactions. However, due to the large amount of information associated with trajectories, quantitative analysis of the dynamic origin of reaction selectivity is complex. For the electrocyclic ring opening of cyclopropyl radical, more than 4000 trajectories were run showing that allyl radicals are formed through a mixture of disrotatory intrinsic reaction coordinate (IRC) motion as well as conrotatory non-IRC motion. Geometric, vibrational mode, and atomic velocity transition-state features from these trajectories were used for supervised machine learning analysis with classification algorithms. Accuracy >80% with a random forest model enabled quantitative and qualitative assessment of transition-state trajectory features controlling disrotatory IRC versus conrotatory non-IRC motion. This analysis revealed that there are two key vibrational modes where their directional combination provides prediction of IRC versus non-IRC motion.

Machine Learning Analysis of Direct Dynamics Trajectory Outcomes for Thermal Deazetization of 2,3-Diazabicyclo[2.2.1]hept-2-ene

Experimentally, the thermal gas-phase deazetization of 2,3-diazabicyclo[2.2.1]hept-2-ene (1) results in the loss of N₂ and the formation of bicyclo products 3 (exo) and 4 (endo) in a nonstatistical ratio, with preference for the exo product. Here, we report unrestricted M06-2X quasiclassical trajectories initialized from the concerted N₂ ejection transition state that were able to replicate the experimental preference to form 3. We found that the 3:4 ratio results from the relative amounts of very fast (ballistic) exotype trajectories versus trajectories that lead to the 1,3-diradical intermediate 2. These quasiclassical trajectories provided a set of transition-state vibrational, velocity, momenta, and geometric features for the machine learning analysis. A selection of popular supervised classification algorithms (e.g., random forest) provided poor prediction of trajectory outcomes based on only transition-state vibrational quanta and energy features. However, these machine learning models provided more accurate predictions using atomic velocities and atomic positions, attaining ∼70% accuracy using initial conditions and between 85 and 95% accuracy at later reaction time steps. This increased accuracy allowed the feature importance analysis to reveal that, at the later-time analysis, the methylene bridge out-of-plane bending is correlated with trajectory outcomes for the formation of either the exo product or toward the diradical intermediate. Possible reasons for the struggle of machine learning algorithms to classify trajectories based on transition-state features is the heavily overlapping feature values, the finite but very large possible vibrational mode combinations, and the possibility of chaos as trajectories propagate. We examined this chaos by comparing a set of nearly identical trajectories that differed by only a very small scaling of the kinetic energies resulting from the transition-state reaction coordinate.

Neural network approach for the dynamics on the normally hyperbolic invariant manifold of periodically driven systems

Chemical reactions in multidimensional systems are often described by a rank-1 saddle, whose stable and unstable manifolds intersect in the normally hyperbolic invariant manifold (NHIM). Trajectories started on the NHIM in principle never leave this manifold when propagated forward or backward in time. However, the numerical investigation of the dynamics on the NHIM is difficult because of the instability of the motion. We apply a neural network to describe time-dependent NHIMs and use this network to stabilize the motion on the NHIM for a periodically driven model system with two degrees of freedom. The method allows us to analyze the dynamics on the NHIM via Poincaré surfaces of section (PSOS) and to determine the transition-state (TS) trajectory as a periodic orbit with the same periodicity as the driving saddle, viz. a fixed point of the PSOS surrounded by near-integrable tori. Based on transition state theory and a Floquet analysis of a periodic TS trajectory we compute the rate constant of the reaction with significantly reduced numerical effort compared to the propagation of a large trajectory ensemble.

Application of Computational Biology and Artificial Intelligence Technologies in Cancer Precision Drug Discovery

Artificial intelligence (AI) proves to have enormous potential in many areas of healthcare including research and chemical discoveries. Using large amounts of aggregated data, the AI can discover and learn further transforming these data into "usable" knowledge. Being well aware of this, the world's leading pharmaceutical companies have already begun to use artificial intelligence to improve their research regarding new drugs. The goal is to exploit modern computational biology and machine learning systems to predict the molecular behaviour and the likelihood of getting a useful drug, thus saving time and money on unnecessary tests. Clinical studies, electronic medical records, high-resolution medical images, and genomic profiles can be used as resources to aid drug development. Pharmaceutical and medical researchers have extensive data sets that can be analyzed by strong AI systems. This review focused on how computational biology and artificial intelligence technologies can be implemented by integrating the knowledge of cancer drugs, drug resistance, next-generation sequencing, genetic variants, and structural biology in the cancer precision drug discovery.

Concepts of Artificial Intelligence for Computer-Assisted Drug Discovery

Artificial intelligence (AI), and, in particular, deep learning as a subcategory of AI, provides opportunities for the discovery and development of innovative drugs. Various machine learning approaches have recently (re)emerged, some of which may be considered instances of domain-specific AI which have been successfully employed for drug discovery and design. This review provides a comprehensive portrayal of these machine learning techniques and of their applications in medicinal chemistry. After introducing the basic principles, alongside some application notes, of the various machine learning algorithms, the current state-of-the art of AI-assisted pharmaceutical discovery is discussed, including applications in structure- and ligand-based virtual screening, de novo drug design, physicochemical and pharmacokinetic property prediction, drug repurposing, and related aspects. Finally, several challenges and limitations of the current methods are summarized, with a view to potential future directions for AI-assisted drug discovery and design.

Post-transition state bifurcations induce dynamical detours in Pummerer-like reactions

A post-transition state bifurcation (PTSB) involved in a Pummerer-type rearrangement is characterized using density functional theory (DFT) calculations on potential energy stationary points and direct dynamics simulations. A sensitivity of the ratio of products produced via this PTSB to solvent dielectric constant is revealed and implications of such a dependence for selectivity control of organic reactions are discussed.

Neural network approach to time-dependent dividing surfaces in classical reaction dynamics

In a dynamical system, the transition between reactants and products is typically mediated by an energy barrier whose properties determine the corresponding pathways and rates. The latter is the flux through a dividing surface (DS) between the two corresponding regions, and it is exact only if it is free of recrossings. For time-independent barriers, the DS can be attached to the top of the corresponding saddle point of the potential energy surface, and in time-dependent systems, the DS is a moving object. The precise determination of these direct reaction rates, e.g., using transition state theory, requires the actual construction of a DS for a given saddle geometry, which is in general a demanding methodical and computational task, especially in high-dimensional systems. In this paper, we demonstrate how such time-dependent, global, and recrossing-free DSs can be constructed using neural networks. In our approach, the neural network uses the bath coordinates and time as input, and it is trained in a way that its output provides the position of the DS along the reaction coordinate. An advantage of this procedure is that, once the neural network is trained, the complete information about the dynamical phase space separation is stored in the network's parameters, and a precise distinction between reactants and products can be made for all possible system configurations, all times, and with little computational effort. We demonstrate this general method for two- and three-dimensional systems and explain its straightforward extension to even more degrees of freedom.

The TensorMol-0.1 model chemistry: a neural network augmented with long-range physics

We construct a robust chemistry consisting of a nearsighted neural network potential, TensorMol-0.1, with screened long-range electrostatic and van der Waals physics. It is offered in an open-source Python package and achieves millihartree accuracy and a scalability to tens-of-thousands of atoms on ordinary laptops.

Traditional force fields cannot model chemical reactivity, and suffer from low generality without re-fitting. Neural network potentials promise to address these problems, offering energies and forces with near ab initio accuracy at low cost. However a data-driven approach is naturally inefficient for long-range interatomic forces that have simple physical formulas. In this manuscript we construct a hybrid model chemistry consisting of a nearsighted neural network potential with screened long-range electrostatic and van der Waals physics. This trained potential, simply dubbed “TensorMol-0.1”, is offered in an open-source Python package capable of many of the simulation types commonly used to study chemistry: geometry optimizations, harmonic spectra, open or periodic molecular dynamics, Monte Carlo, and nudged elastic band calculations. We describe the robustness and speed of the package, demonstrating its millihartree accuracy and scalability to tens-of-thousands of atoms on ordinary laptops. We demonstrate the performance of the model by reproducing vibrational spectra, and simulating the molecular dynamics of a protein. Our comparisons with electronic structure theory and experimental data demonstrate that neural network molecular dynamics is poised to become an important tool for molecular simulation, lowering the resource barrier to simulating chemistry.