Jul 2026· Machine Learning: Science and Technology· Vol 7, pp. 045039· 0 citations· 25 references
Physics
TL;DR
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.
Abstract
Machine learning (ML) is increasingly utilized in molecular dynamics (MD) simulations to investigate complex system properties across disciplines ranging from chemical and physical sciences to engineering. However, these methods often require large datasets for model training and may not fully adhere to physical principles, limiting their scientific explainability. Furthermore, the model training remains highly challenging under sparse data. To overcome these limitations, this paper introduces the Molecular Physics-Informed Neural Network (mPINN) framework, designed to solve Newton’s equations of motion for multi-body atomistic interactions without relying on prior observational time-series data. By directly embedding the governing principles of MDs into the neural network training process, the mPINN promotes physical consistency, ensuring that predicted trajectories adhere to conserved thermodynamic quantities. This methodology replaces unconstrained empirical data-fitting with mathematically bound physical relationships, yielding stable and physically valid performance across continuous temporal domains. Unlike traditional MD engines that rely on step-by-step discrete integration, the mPINN operates within a continuous time framework during each training iteration. This approach effectively alleviates issues related to timestep selection and stability commonly faced in discrete simulations. 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.
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.
Petros Triantafyllos, P. Krokidas, C. Rekatsinas· 0 citations
In multiscale modeling of ferroelectrics, combining atomistic simulation with continuum-scale phase-field models (PFM) remains a fundamental challenge. A key difficulty lies in faithfully capturing discrete atomic-level information within a continuum modeling framework, while accurately representing material behavior at the mesoscale. In this paper, a Physics-Informed Neural Network (PINN) driven by molecular dynamics (MD) data is used. The loss function of the network consists of a supervised term that fits the discrete spatial polarization distributions obtained from MD simulations of systems containing domain walls, and a physics-based term that incorporates the residuals of partial differential equations (PDEs) of steady-state PFM. To ensure stable and balanced training among the different loss components, adaptive gradient normalization (GradNorm) is used to dynamically adjust the task weights. By minimizing the total loss, the model not only reconstructs the polarization field along with the associated strain, stress, and energy landscape at the continuum scale, but also identifies critical physical parameters of the phase-field model, including the characteristic energy density, characteristic length factor, gradient energy anisotropy factor, and Landau polynomial coefficients. By using the PINN-predicted physical parameters in COMSOL Multiphysics to solve the corresponding PDEs within a finite element framework, we demonstrate that these parameters enable accurate reproduction of the ferroelectric domain structure and the associated material response, including stress/strain distributions and energy landscape. This framework provides an effective methodology for establishing multiscale connections between atomistic and continuum descriptions, and holds the potential to infer underlying physical properties directly from polarization distributions for a wide range of materials.
Xuejian Wang, Frank Wendler, Hikaru Auzuma et al.· 0 citations
Physics-informed neural networks (PINNs) have emerged as a powerful paradigm in scientific machine learning by embedding governing physical laws into neural network training through loss functions. They have demonstrated remarkable success in solving various forward and inverse problems governed by partial differential equations (PDEs). However, in practical applications, purely physics-constrained PINNs that rely solely on PDE residuals often suffer from slow or non-convergence and limited prediction accuracy, particularly when modeling high-order dynamical systems (e.g., second-order and above). Moreover, conventional PINNs struggle to effectively capture high-frequency components in complex physical fields, which further limits their generalization and representational capability.
To address these challenges, this study proposes a data-guided physics-informed neural network with Fourier feature enhancement. In the proposed framework, a small amount of high-fidelity measurement or simulation data is incorporated to guide the training process, providing explicit guidance that complement the physics-based constraints. Meanwhile, Fourier feature embeddings are introduced into the input layer of the network to enhance its ability to represent high-frequency variations and multi-scale solution structures. This synergistic integration of data guidance and Fourier-enhanced representations accelerates convergence, improves robustness, and enhances the accuracy of PDE solutions.
The effectiveness of the proposed PINN model is validated through numerical and simulation studies on Euler-Bernoulli beam vibration problems, which serve as representative examples of high-order mechanical systems. The results demonstrate that PINN achieves more accurate and stable full-field vibration reconstructions than conventional PINNs, particularly under conditions involving high-frequency modes. These findings highlight the potential of hybrid data-physics neural frameworks as an efficient and reliable approach for solving complex PDE-governed dynamical systems.
Hailong Liu, S. Hedayatrasa, Yunpeng Zhu et al.· e-Journal of Nondestructive...· 0 citations
Tumor progression is an inherently multiphysical phenomenon in which interstitial fluid dynamics, biochemical transport, and cellular mechanics interact across multiple spatiotemporal scales. Classical mesh-based solvers, although accurate, impose prohibitive computational costs for the repeated evaluations demanded by inverse parameter identification and future patient-specific predictive pipelines. In this work we introduce a Physics-Informed Neural Network (PINN) framework for a tractable chemo-fluidic continuum model of tumor growth that couples an advection-diffusion-reaction (ADR) equation for the tumor volume fraction with a quasi-static Darcy pressure equation for the interstitial fluid pressure. By intentionally decoupling the solid-mechanical equilibrium, we obtain a three-equation system whose gradient structure is stable under automatic differentiation, enabling robust deep-learning optimization. The network simultaneously learns both state variables from physics constraints alone (forward problem) and recovers hidden transport parameters from sparse, noisy synthetic measurements (Data-Assimilation PINN, DA-PINN, inverse problem). We verify the forward solver against a high-resolution finite-difference (FD) reference, achieving a mean absolute error below 0.002. For the inverse problem, starting from an initial permeability estimate of 0.08 (a factor of 4x above the true value of 0.02) with only 5% spatially sparse observations corrupted by 5% Gaussian noise, the DA-PINN recovers the permeability with a relative error below 5%. These results demonstrate that physics-informed deep learning constitutes a viable, computationally efficient route to multiphysics oncology modeling and lays the mathematical groundwork for future integration into clinical data assimilation pipelines.
Celia Taboada, Pedro Navas, M. Molinos· 0 citations
The quantitative prediction of biomolecular recognition is crucial to molecular science. The challenge is not merely structural determination but the prediction of (thermo)dynamic and kinetic observables arising from high-dimensional molecular ensembles, such as free energies, conformational distributions, and rate processes across different conditions. As the field shifts from structure-centric to ensemble-based descriptions, two complementary modeling strategies have matured: explicit energy-based approaches grounded in statistical mechanics and data-driven models that learn statistical representations of molecular configurations from large data sets. Physics-based methods, including molecular dynamics and free energy perturbation, estimate observables by sampling (Boltzmann-distributed) configurations under approximate molecular Hamiltonians, thereby providing mechanistic interpretability and thermodynamic consistency, albeit at non-negligible computational cost and with inherent force field limitations. In contrast, modern machine learning approaches rapidly generate structures and propose conformational ensembles without explicit thermodynamic weighting, by learning statistical patterns in structural and bioactivity data. While these methods often achieve high predictive performance, they do not inherently enforce thermodynamic consistency due to the lack of an explicit connection to a partition function and thus may produce configurations that are not physically realizable. We argue that, since physics-based simulations and machine learning provide complementary approximations to the underlying probability distribution associated with biomolecular recognition events, and they excel respectively in consistency with free-energy landscapes and state populations and in predictive accuracy, the central challenge for the coming decade will be integrating them into hybrid frameworks that are scalable and transferable.
R. Khalil, Elena Frasnetti, Han Kurt et al.· Journal of Physical Chemistr...· 0 citations
We introduce implicit machine learning force fields (I-MLFFs), which replace explicit stacks of neural network layers with self-consistent fixed-point equations. In molecular simulations, this formulation enables intermediate representations to be reused across successive timesteps, thereby warm-starting force evaluation. The resulting models effectively combine the computational footprint of a shallow, single-layer MLFF with the representational capacity and accuracy of a deep neural network. Our approach unlocks architecture-agnostic efficiency gains that are inaccessible when force prediction and trajectory integration are considered separately. We demonstrate this across three major classes of graph neural networks: invariant, equivariant Cartesian tensor, and SO(3)-equivariant spherical-tensor architectures. Each yields a two- to five-fold reduction in compute and memory footprint. Crucially, these gains are achieved while retaining full atomistic resolution and the original integration timestep, avoiding spatial or temporal coarse graining. Our contribution therefore advances the scaling frontier of quantum-mechanically faithful molecular simulation, enabling longer trajectories and larger atomistic systems within fixed GPU memory and compute budgets, and thereby opening access to new insights across biomolecular and material systems.
J. Maess, Leon Werner, J. Frank et al.· 0 citations