arXiv:2608. 04222v1 Announce Type: cross Abstract: Turbulence is a central testbed for machine learning on physical dynamics because its governing laws are known exactly.
arXiv:2607. 13022v1 Announce Type: cross Abstract: Many nonlinear physical systems exhibit an initial transient phase in which perturbations grow before nonlinear interactions lead to a statistically steady state.
Many nonlinear physical systems exhibit an initial transient phase in which perturbations grow before nonlinear interactions lead to a statistically steady state. While this saturated regime is of primary interest, direct numerical simulations must resolve the full transient dynamics before reaching it, incurring significant computational cost.
arXiv:2510.01365v2 Announce Type: replace Abstract: The ability to model mechanics of soft materials under flowing conditions is key in designing and engineering processes and materials with targeted...
arXiv:2609.24947v1 Announce Type: new Abstract: Neural operators evaluate parametric partial differential equations cheaply but degrade sharply outside their training distribution. Physics-informed n...
arXiv:2607. 02194v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) have emerged as a promising route to solve partial differential equations, yet they have struggled to reach the precision of classical solvers.
arXiv:2603. 08465v3 Announce Type: replace Abstract: While Physics-Informed Neural Networks (PINNs) offer a mesh-free approach to solving fluid-flow PDEs, standard point-wise residual minimization suffers from convergence pathologies in topologically complex domains like Triply Periodic Minimal Surfaces (TPMS).
The paper introduces a two-part neural framework for generating and analyzing forced three-dimensional incompressible Navier–Stokes flow. Part I focuses on a physics‑informed neural model that produces structured external‑force trajectories, optimizes them via differentiable PDE rollouts or PPO‑Clip, and validates selected forcings through fixed‑force replay. Part II provides a mathematical certification layer that separates neural candidate discovery from continuum analysis, derives integrated reciprocal‑vorticity criteria implying Riccati‑type growth and finite‑time loss of smooth continuation, and establishes a conditional positive‑probability closure for a nondegenerate neural output law, completing the proof at the continuum level.
arXiv:2512. 19643v2 Announce Type: replace Abstract: Numerical simulation of time-dependent partial differential equations (PDEs) is central to scientific and engineering applications, but high-fidelity solvers are often prohibitively expensive for long-horizon or time-critical settings.
arXiv:2604. 23874v3 Announce Type: replace-cross Abstract: The differentiable physics paradigm may be leveraged as an a-posteriori approach for discovering turbulence closure models by embedding a neural network parameterization directly inside the solver and optimizing it given potentially sparse target data.
arXiv:2608.29069v1 Announce Type: cross Abstract: Operator-learning surrogates have been benchmarked largely on single-field, single-interface problems, leaving unclear whether architectural choices...
arXiv:2510. 25306v3 Announce Type: replace Abstract: Partial physical knowledge--governing structures known, constitutive relations or their combinations not--pervades spatiotemporal systems.