arXiv:2608. 04384v1 Announce Type: new Abstract: Neural PDE solver auto-design is fundamentally a search-space representation problem.
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arXiv:2606. 10752v1 Announce Type: new Abstract: Numerical solvers for partial differential equations (PDEs) are core computational tools in science and engineering.
arXiv:2511. 22651v2 Announce Type: replace-cross Abstract: Optimization methods have long advanced many fields, yet they struggle when faced with design problems where the search space and design parameters are difficult to define.
arXiv:2608. 03600v1 Announce Type: new Abstract: Partial differential equations (PDEs) become actionable in science and engineering not as isolated formulae, but as executable workflows that connect modelling assumptions, governing equations, numerical solvers, diagnostics, and decisions.
arXiv:2607. 18252v1 Announce Type: new Abstract: Machine learning methods have shown that data-driven policies can accelerate mixed-integer linear programming (MILP) solvers, but many such approaches remain difficult to inspect, adapt, and deploy because the learned policy is represented as an external predictor or other opaque model.
arXiv:2607. 26490v1 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs), yet their performance heavily relies on the manual, trial-and-error engineering of neural representations, loss formulations, and optimization dynamics.
arXiv:2607. 18256v1 Announce Type: new Abstract: Optimization modeling is the process of translating real-world decision problems, often described in natural language, into formal mathematical formulations and executable solver code.