The results indicate that physically meaningful molecular trajectories can emerge directly from physics-only supervision, supporting the feasibility of trajectory-unsupervised neural solvers for molecular dynamics.
Abstract
Molecular dynamics (MD) simulations are governed by explicit equations of motion, yet most neural approaches that accelerate or emulate MD rely on simulator-generated trajectories, forces, or energies for training. In this work we ask to what extent can physically meaningful molecular trajectories be recovered from the governing laws. We introduce the Differentiable Newtonian Molecular Solver (DINaMo), a physics-informed neural framework that represents molecular trajectories as differentiable functions of time and is trained exclusively through Newtonian dynamics, conservation laws, and analytic interaction potentials on a given equilibrated initial state. Unlike prior physics-informed MD formulations, DINaMo uses no simulator-generated trajectories, forces, velocities, or energies as supervisory targets. In Lennard--Jones argon systems, the learned trajectories reproduce short-time coordinate, energy, and structural observables, including in a larger and denser liquid-like setting where the radial distribution function is recovered. Although currently limited to short temporal horizons, the results indicate that physically meaningful molecular trajectories can emerge directly from physics-only supervision, supporting the feasibility of trajectory-unsupervised neural solvers for molecular dynamics.
The results demonstrate that the mPINN architecture functions as a reliable, physics-constrained ML framework capable of delivering high-fidelity trajectory predictions for complex multi-body molecular systems.
T. Muther, Vuong Van Pham, A. K. Dahaghi· Machine Learning: Science an...· 0 citations
A physics-informed neural operator framework is introduced that predicts the LBE evolution over large time jumps without performing step-by-step forward integration, bypassing the need to solve the collision kernel explicitly.
Xiao Xue, Marco F. P. ten Eikelder, Mingyang Gao et al.· Nature Communications· 0 citations
Experiments on real deformable-object manipulation sequences show that PhysCoRe outperforms state-of-the-art baselines in prediction accuracy, and that its predicted confidence forms a reliable distribution across the object's geometry, providing a natural signal for future confidence-guided exploration.
The Fokker-Planck partial differential equation (FP-PDE) governs uncertainty evolution in stochastic dynamical systems. In orbital dynamics, solving the FP-PDE is challenging because of nonlinear motion, high-dimensional states, and large space-time domains. We develop a physics-informed neural network (PINN) approach that approximates the FP-PDE solution as a single space-time probability density, while also quantifying its worst-case approximation error. This approach is, in principle, independent of the choice of state coordinates and neural network architecture. Specifically, to enforce probability density function (PDF) properties into the neural network, we design a Physics-informed Gaussian mixture model (PINN-GMM). Then a companion error PINN learns the dynamics of the approximation error and yields time-dependent bounds that define an ambiguity set of PDFs. This ambiguity set enables rigorous computation of upper and lower bounds on event probabilities through tractable linear programs. Numerical studies on illustrative 1D examples and several 4D--6D orbital test cases demonstrate accurate uncertainty propagation, correct and informative error bounds, and improved reliability over common uncertainty-propagation baseline methods (Gaussian approximation, unscented transform, and Gaussian mixture model). Constructing the PINN-GMM requires offline training, making it costlier than the baseline approximations; once trained, however, a single forward pass returns the density at any time in sub-millisecond time $(0.16~\mathrm{ms}$ in our implementation).
Chun-Wei Kong, Morteza Lahijanian, Jay W. McMahon· 0 citations
The demand for high-fidelity, physically-based animation has traditionally been met by sophisticated solvers rooted in elastodynamics and finite element analysis (FEM). Recently, the emergence of neural physics has led to a paradigm shift, transforming neural networks into solvers with memory that dramatically increase the scale and speed of digital environments. Despite its reputation, physics-based simulation does not have to be intimidating. This course aims to demystify the field, proving that these complex systems are accessible and intuitive when approached correctly. We provide a unified journey from classical formulations to modern neural techniques, grounding the audience in the fundamentals of elastostatics and dynamics. We demonstrate how physical problems are discretized via linear finite elements and solved through the elegant lens of optimization. Transitioning into neural physics, we showcase how traditional simulation knowledge translates directly into machine learning loss functions and neural architectures. We analyze strategies for modeling latent spaces for a system’s equilibrium states and to create truly controllable, real-time frameworks. Designed for a broad audience—including students, engineers, researchers, and artists—this course balances theory with practice. To ensure these concepts are immediately actionable, we provide comprehensive reference code for all discussed methods. By the end of the session, attendees will possess the tools to quickly and easily implement their own physics solvers, empowering them to build the next generation of physics-enhanced frameworks and interactive worlds.
D. Corigliano, Otman Benchekroun, J. Barbič· Proceedings of the Special I...· 0 citations
Classical numerical solvers for partial differential equations (PDEs) are computationally expensive to solve repeatedly across varying initial conditions, motivating the need for learned surrogates. In this paper, we propose a trainable Neural Cellular Automata (NCA) based surrogate model for learning long time PDE dynamics. Rather than mapping an entire initial field to a full trajectory in one shot, our proposed model learns a small, local, homogeneous update rule that is applied identically and repeatedly at every grid cell, mirroring the locality of differential operators. We benchmark this framework against three baselines: PDE - Net, a modified physics-informed neural network (PINN), and a Fourier Neural Operator (FNO), on five canonical PDEs (heat, advection, Burgers, Allen - Cahn, and Fisher - KPP), evaluated at temporal domain two times beyond the training temporal domain. The proposed model achieves the lowest long-horizon relative errors on the majority of the experiments.
Esha Saha, Hao Wang· 0 citations
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