arXiv:2608. 11279v1 Announce Type: new Abstract: Basin is a numerical optimization library for the Rust programming language.
Basin is a numerical optimization library for the Rust programming language. Numerical optimization is the task of finding the inputs that minimize a function, and it is a fundamental element across the sciences: fitting a model to data, calibrating a simulation, training a machine learning model, or choosing engineering parameters that minimize cost.
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: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:2607. 13921v1 Announce Type: cross Abstract: Languages with rich static semantics, such as Rust, provide stronger guarantees for AI-generated code, but their strictness makes generation more difficult.
arXiv:2608. 08156v1 Announce Type: new Abstract: In evolutionary algorithms powered by language models, the LLM acts as a single operator that simultaneously updates structural components (like control flow) and continuous parameters.
arXiv:2606. 30328v1 Announce Type: cross Abstract: Rapid prototyping of algorithms is a critical step in modern machine learning.
arXiv:2509. 08765v4 Announce Type: replace-cross Abstract: Data-driven acceleration of scientific computing workflows has been a high-profile aim of machine learning (ML) for science, with numerical simulation of transient partial differential equations (PDEs) being one of the main applications.
arXiv:2601. 10222v2 Announce Type: replace-cross Abstract: Optimization is central to both modern machine learning (ML) and scientific machine learning (SciML), yet the structure of the underlying optimization problems differs substantially across these domains.
arXiv:2605. 25001v2 Announce Type: replace Abstract: While Physics-Informed Neural Networks (PINNs) are powerful for solving Partial Differential Equations (PDEs), their training is often paralyzed by gradient pathology.
arXiv:2607. 13652v1 Announce Type: new Abstract: Many design tasks can be cast as black-box function optimization, enabling use of Bayesian optimization to find an ideal design with minimal number of trials.
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: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.