arXiv:2605. 04853v2 Announce Type: replace Abstract: We propose HIN-LRI, a hybrid framework that augments a classical numerical solver with a neural operator trained to correct the solver's structured truncation error.
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:2606. 27354v1 Announce Type: cross Abstract: Neural surrogate models offer fast approximate mappings from PDE parameters to solutions, but they typically treat solving as a purely statistical task: once trained, they struggle to correct their own constraint violations and extrapolate beyond the training distribution.
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:2606. 01122v1 Announce Type: new Abstract: We propose a five-step diagnostic protocol for residual-trained neural HJB-PIDE solvers with control-dependent L\'evy jumps, targeting a general failure mode of neural PDE methods: a learned solution can match headline scalar diagnostics while miscomputing an operator inside its training loss.
arXiv:2606. 18175v1 Announce Type: cross Abstract: We present a numerical method for the forward solution of nonlinear partial differential equations (PDEs) in which Bellman-Kalaba quasilinearization reduces the nonlinear problem to a sequence of linear subproblems, each discretized by collocation onto a trial space that is linear in its parameters and solved by a single direct linear least-squares QR factorization.
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:2605. 23391v2 Announce Type: replace Abstract: Physics-informed neural networks (PINNs) for coupled multiphysics systems suffer systematic accuracy degradation as inter-equation coupling strengthens.
arXiv:2606. 12337v1 Announce Type: cross Abstract: Inverse problems governed by partial differential equations (PDEs) are central to computational mechanics and are commonly solved by adjoint-based optimization, while physics-informed neural networks (PINNs) have emerged as a flexible alternative.
arXiv:2602.08515v3 Announce Type: replace-cross Abstract: This work investigates shallow physics-informed neural networks (PINNs) for solving forward and inverse problems governed by nonlinear partia...
arXiv:2609.24021v1 Announce Type: cross Abstract: Neural operators are data-driven models that learn mappings from inputs that parameterize partial differential equations, such as spatially varying c...
arXiv:2607. 15291v1 Announce Type: cross Abstract: We develop a physics-informed neural network (PINN) framework for nonlocal partial differential equations arising in dynamic density functional theory (DDFT).
arXiv:2601. 20496v2 Announce Type: replace-cross Abstract: Generating dense physical fields from sparse measurements is a fundamental question in sampling, signal processing, and many other applications.