arXiv:2607. 22004v1 Announce Type: new Abstract: Energy natural gradient descent (ENGD) aligns parameter updates with the curvature of an underlying function-space energy, but existing formulations assume an unconstrained Euclidean parameter domain.
arXiv:2606. 27895v1 Announce Type: cross Abstract: Differentiable partial differential equation (PDE) solvers underpin solver-in-the-loop ML training, gradient-based optimal control, and inverse problems, yet the practical cost of obtaining correct, usable gradients from a given solver on a given problem is largely undocumented.
arXiv:2609.36165v1 Announce Type: cross Abstract: In this work, we develop a second-order optimization framework for physics-informed neural networks (PINNs) applied to high-dimensional parametric pa...
arXiv:2607. 00095v1 Announce Type: cross Abstract: Generative models have emerged as scalable surrogates for physical simulation, yet they offer no guarantee that their outputs respect the conservation laws, boundary conditions, and nonlinear invariants that govern the underlying physics.
arXiv:2606. 10562v1 Announce Type: cross Abstract: We propose a new optimization method, the Nystr\"om-enhanced relaxed scalar auxiliary variable method (N-RSAV), which incorporates curvature information into the RSAV framework to accelerate convergence while preserving an unconditional modified energy dissipation law.
Nonlinear least-squares optimization is central to regression, physics-informed neural networks, and other machine-learning tasks. Such problems have a natural geometric interpretation, model predictions form a manifold in data space, while the chosen parameterization can introduce parameter-effects curvature that becomes a dominant source of nonlinearity.
arXiv:2607. 20378v1 Announce Type: new Abstract: Physics-informed learning of partial differential equations (PDEs) has been dominated by multilayer perceptrons (MLPs), whose spectral bias and dense parameterization limit both accuracy and interpretability.
arXiv:2607. 22215v1 Announce Type: new Abstract: In this study, we introduce latent PDE mapping, a broadly applicable physics-informed learning technique designed to enable efficient geometric generalization with sparse training data.
The paper introduces the Physics-Informed Stochastic Configuration Machine (PI‑SCM), a backpropagation‑free neural network designed for solving nonlinear differential equations. By analytically evaluating local Jacobians, PI‑SCM linearizes the physical loss, enabling optimal weight determination through generalized linear least squares and avoiding iterative nonlinear optimization. The authors present a progressive algorithmic suite—PI‑SC‑I, PI‑SC‑II, and PI‑SC‑III—prove their universal approximation properties, and show through experiments that PI‑SCM achieves high‑fidelity predictions and parameter identification while accelerating training by orders of magnitude compared to standard PINNs.
arXiv:2607. 07623v1 Announce Type: new Abstract: Nonlinear least-squares optimization is central to regression, physics-informed neural networks, and other machine-learning tasks.
arXiv:2601. 21487v2 Announce Type: replace-cross Abstract: We study minimization of smooth functions over feasible sets that have smooth embedded-manifold structure throughout or only on selected regions, using linear minimization oracles (LMOs) to determine search directions under user-chosen norms.
arXiv:2609.40287v1 Announce Type: new Abstract: Physics-constrained generative models aim to generate physical fields that match a target distribution and satisfy prescribed constraints. However, enf...
arXiv:2606. 12120v1 Announce Type: new Abstract: Low-rank optimal transport (OT) mitigates the quadratic scaling of classical solvers, yet existing approaches rely heavily on first-order mirror-descent updates that require careful hyperparameter tuning and ignore the optimization landscape's curvature.