Lagrangian Neural Networks (LNNs) can learn irreducible three‑body interactions from trajectory data by parameterizing only the potential while prescribing kinetic energy. Using the Axilrod‑Teller triple‑dipole interaction as a test case, the authors show that a signal‑aware sampling strategy allows the LNN to recover the correct radial scaling, angular dependence, and sign reversal from accelerations alone. Symbolic regression on the trained potential reproduces the exact Axilrod‑Teller expression, demonstrating that LNNs can uncover closed‑form many‑body laws without prior functional assumptions.
arXiv:2510. 25306v3 Announce Type: replace Abstract: Partial physical knowledge--governing structures known, constitutive relations or their combinations not--pervades spatiotemporal systems.
arXiv:2608. 13215v1 Announce Type: new Abstract: Forecasting the long-horizon evolution of mechanical systems from position-only observations is a pivotal yet difficult task, as hidden velocities and trajectory-specific physical properties must be inferred simultaneously.
arXiv:2609.37113v1 Announce Type: new Abstract: Generalized reaction-diffusion systems encompass diverse transport mechanisms and coupled reaction kinetics. A central question for neural PDE solvers...
The paper introduces Newmark‑eta‑DGN, a graph neural network framework that learns coarse‑step dynamics and internal mechanical responses from discretely sampled trajectories. It combines a semi‑implicit update inspired by the Newmark‑eta method with an operator‑weighted virtual hub to capture system‑wide coupling. The model can predict long‑horizon motion and infer unobserved forces and stiffness operators across deformable beams, human gait, and protein dynamics without explicit supervision on mechanical quantities.
arXiv:2606. 04100v1 Announce Type: new Abstract: Machine learning interatomic potentials (MLIPs) enable efficient and accurate atomistic simulations but depend critically on the quality and diversity of the training data.
arXiv:2608. 10235v1 Announce Type: new Abstract: Hamiltonian Neural Networks (HNNs) parameterize conservative dynamics through a learned scalar Hamiltonian, providing an architectural prior that is absent from generic vector-field neural networks.
The paper introduces MVNN, a measure‑valued neural network designed to learn interaction forces in systems governed by McKean‑Vlasov dynamics directly from particle trajectory data. MVNN extends conventional neural networks to operate on probability measures by learning cylindrical features through an embedding network that maps distributions to scalable vector representations. The authors prove theoretical properties such as well‑posedness, propagation‑of‑chaos, universal approximation, and provide quantitative rates under low‑dimensional measure‑dependence, while demonstrating the method’s accuracy and strong out‑of‑distribution generalization on various first‑ and second‑order dynamical systems.
arXiv:2608. 13506v1 Announce Type: cross Abstract: Liquids exhibit collective behavior that depends sensitively on thermodynamic conditions, interfaces and confinement, yet predicting each new state commonly requires a separate atomistic simulation.
arXiv:2609.06546v1 Announce Type: cross Abstract: Although machine learning can be used to predict the evolution of physical systems from data, a formulation that learns only the system state at each...
arXiv:2602. 12706v2 Announce Type: replace Abstract: Neural operators have emerged as fast surrogate solvers for parametric partial differential equations (PDEs).
arXiv:2607. 03671v1 Announce Type: cross Abstract: Models of complex systems often have many parameters, yet are constrained by far fewer experimentally accessible observables: similar activity can emerge from coordinated parameter changes.
The paper presents a multitask learning approach that incorporates orbitally resolved semiempirical charges into machine learning interatomic potentials (MLIPs). By training with inexpensive GFN1‑xTB orbital charges, the model reduces energy mean absolute error by 58% compared to energy‑only baselines and needs five times less data to achieve similar performance. The method also outperforms or matches models using costly DFT charges and preserves inference efficiency, offering a scalable way to build accurate, data‑efficient foundation models for complex chemical systems.