arXiv:2608. 12624v1 Announce Type: new Abstract: Structure-preserving machine learning embeds physical structure directly into model architectures, yet uncertainty quantification (UQ) for such hard-constrained models remains limited because standard UQ methods may violate the encoded admissibility conditions, require architectural modifications, or impose substantial computational costs.
arXiv:2510. 25306v3 Announce Type: replace Abstract: Partial physical knowledge--governing structures known, constitutive relations or their combinations not--pervades spatiotemporal systems.
arXiv:2609.35884v1 Announce Type: new Abstract: Divergence-free vector fields are fundamental state variables in incompressible flows and many PDE systems. Redundant parameterizations, including Neur...
arXiv:2604. 07366v2 Announce Type: replace Abstract: Partial differential equations (PDEs) govern nearly every physical process in science and engineering, but solving them at scale remains prohibitively expensive.
arXiv:2606. 11650v1 Announce Type: new Abstract: Recent advances in scientific machine learning provide a means of near-real-time solution to partial differential equations (PDEs), but lack the theoretical underpinnings of conventional simulators that support contemporary verification and validation.
This paper extends the hard constraint projection (HCP) method to the nonlinear 1D Burgers' equation, integrating it into a physics‑informed neural network (PINN). By discretising the equation, constructing a constraint matrix, and adding an unlearnable projection layer, the HCP‑PINN enforces the governing PDE during training. Experiments show that the HCP‑PINN achieves higher accuracy—about an order of magnitude lower data error than a standard PINN—and better adherence to the PDE, while being less sensitive to the number and placement of collocation points.
arXiv:2608.31028v1 Announce Type: cross Abstract: Scientific discovery often requires reasoning over competing hypotheses that are consistent with experimental observations. For mixed-variable and co...
arXiv:2606. 06171v1 Announce Type: cross Abstract: Physics-Informed Neural Networks inherently suffer from task interference because they rely on a shared parameter space to satisfy both governing differential equations and boundary conditions.
arXiv:2605. 15995v2 Announce Type: replace-cross Abstract: Learning latent representations from complex data is central to modern machine learning, spanning temporal, multimodal, and partially observed systems.
arXiv:2611.05735v1 Announce Type: new Abstract: Neural operators fit their representation of functions to the task they are trained on, so every new task rebuilds a reduced space from labeled data. F...
The paper demonstrates that learned simulators can fail in two distinct ways when conditions change: long‑horizon drift due to accumulated errors and incorrect responses to interventions on physical parameters. By adding a symplectic integrator to preserve conservative dynamics, rollouts remain stable for up to 100× the training horizon, while encoding physical coupling via explicit linear factorization allows the model to generalize to unseen signs of that coupling. The study shows that stability and counterfactual generalization arise from separate structural choices, enabling designers to impose each property independently.
arXiv:2503.19081v2 Announce Type: replace Abstract: Scientific foundation models (SciFMs) aim to learn generalizable representations of physical systems governed by partial differential equations (PD...