arXiv:2608. 04384v1 Announce Type: new Abstract: Neural PDE solver auto-design is fundamentally a search-space representation problem.
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.
arXiv:2606. 02863v1 Announce Type: new Abstract: AI-Driven Research Systems (ADRS) -- systems coupling LLMs with automated evaluation to discover algorithms, proofs, and designs -- are being optimized and adopted across domains, but the tools to analyze them have not kept pace.
arXiv:2607. 10474v1 Announce Type: cross Abstract: Partial differential equations (PDEs) are foundational to modeling in science and engineering, but constructing reliable numerical solvers remains labor-intensive, demanding expert knowledge of discretization schemes, stability conditions, and boundary treatments.
arXiv:2602. 15983v3 Announce Type: replace-cross Abstract: Large language models (LLMs) can translate natural language into optimization code, but silent failures pose a critical risk: code that executes and returns solver-feasible solutions may encode semantically incorrect formulations---a feasibility--correctness gap reaching 90 percentage points on compositional problems.
arXiv:2506. 02594v2 Announce Type: replace Abstract: Large language models (LLMs) are increasingly used to synthesize heuristic programs, yet most existing pipelines optimize solvers against fixed benchmark distributions.
arXiv:2607. 03451v1 Announce Type: cross Abstract: While skill optimization for autonomous agents has gained traction, existing methods rely on complex pipelines.
arXiv:2603. 23420v2 Announce Type: replace Abstract: If autoresearch is itself a form of research, then autoresearch can be applied to research itself.