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:2608. 03927v1 Announce Type: new Abstract: Engineered Skeletal Muscle Tissues (ESMs) have become a key structure for biomedical disease modeling and pharmacological screening, yet their functional characterization often relies on simplistic metrics like peak force, discarding critical kinetic information.
The paper presents a method for accurately simulating soft tissue deformation and predicting forces across varying material stiffnesses and geometries. It calibrates hyperelastic constitutive models in the SOFA Framework using gravity‑loaded silicone beams, then trains a softness‑conditioned equivariant graph neural network on the calibrated simulations. The resulting model achieves sub‑millimeter deformation accuracy with 0.010 s inference time, and demonstrates that force prediction quality depends on consistent upstream calibration.
arXiv:2507. 09766v2 Announce Type: replace-cross Abstract: Accurate estimation of Remaining Useful Life (RUL) and State of Health (SoH) is essential for reliable Prognostics and Health Management (PHM), supporting timely maintenance and dependable industrial operation.
arXiv:2509.12151v3 Announce Type: replace-cross Abstract: We present a learnable physics-based model that predicts motion of the robot end effector and reaction force-torque in contact-rich manipulat...
arXiv:2607. 15180v1 Announce Type: new Abstract: Ordinary differential equations (ODEs) are widely used to model dynamical systems in physics, biology, neuroscience, and physiology, but in many applications some equations of the dynamics are unknown and only a subset of the state variables are measured.
arXiv:2606. 09432v1 Announce Type: new Abstract: Modeling interacting dynamical systems requires capturing spatial interactions alongside long-range temporal dependencies.
arXiv:2508. 18173v2 Announce Type: replace Abstract: The discovery of symbolic governing equations is a central goal in science; yet, it remains challenging particularly for graph dynamical systems, where the network topology further shapes the system behavior.
The paper introduces Fundamental Dynamical Units (FDUs), signed three‑node interaction patterns that reduce the combinatorial complexity of interaction architectures in networked dynamical systems. By embedding FDU‑regularized structural inference into a physics‑informed neural ODE, the authors jointly recover interaction structure and perturbation‑resolved trajectories, demonstrating the approach on synthetic benchmarks. This framework enables motif‑prescribed intervention design and mechanistically interpretable inference in complex systems.
The paper introduces a linearized Physics-Informed Neural Network (lPINN), a reduced‑order neural basis approach for solving forward and inverse differential equations. In an offline phase, lPINN learns continuous, differentiable neural basis functions from numerical solutions, which are then frozen for new problem instances; the online solution is obtained by minimizing the governing‑equation residual with additional constraints. Experiments on advection‑diffusion, Burgers', and nonlinear pendulum equations show that lPINN achieves lower solution and parameter errors than vanilla PINNs while reducing online inference times by up to three orders of magnitude, and its continuous representation generalizes to finer meshes without retraining.
arXiv:2606. 10909v1 Announce Type: cross Abstract: Reconstructing local stress fields in heterogeneous microstructures under non-linear, history-dependent loading remains a major computational bottleneck in multi-scale simulations.
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:2607. 29158v1 Announce Type: cross Abstract: We introduce implicit machine learning force fields (I-MLFFs), which replace explicit stacks of neural network layers with self-consistent fixed-point equations.