SciML Agents: Write the Solver, Not the Solution

• URL: http://arxiv.org/abs/2509.09936v1
• Date: Fri, 12 Sep 2025 02:53:57 GMT
• Title: SciML Agents: Write the Solver, Not the Solution
• Authors: Saarth Gaonkar, Xiang Zheng, Haocheng Xi, Rishabh Tiwari, Kurt Keutzer, Dmitriy Morozov, Michael W. Mahoney, Amir Gholami,
• Abstract summary: We introduce two new datasets: a diagnostic dataset of adversarial "misleading" problems; and a large-scale benchmark of 1,000 diverse ODE tasks.<n>We evaluate open- and closed-source LLM models along two axes: (i) unguided versus guided prompting with domain-specific knowledge; and (ii) off-the-shelf versus fine-tuned variants.<n>Preliminary results indicate that careful prompting and fine-tuning can yield a specialized LLM agent capable of reliably solving simple ODE problems.
• Score: 69.5021018644143
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Recent work in scientific machine learning aims to tackle scientific tasks directly by predicting target values with neural networks (e.g., physics-informed neural networks, neural ODEs, neural operators, etc.), but attaining high accuracy and robustness has been challenging. We explore an alternative view: use LLMs to write code that leverages decades of numerical algorithms. This shifts the burden from learning a solution function to making domain-aware numerical choices. We ask whether LLMs can act as SciML agents that, given a natural-language ODE description, generate runnable code that is scientifically appropriate, selecting suitable solvers (stiff vs. non-stiff), and enforcing stability checks. There is currently no benchmark to measure this kind of capability for scientific computing tasks. As such, we first introduce two new datasets: a diagnostic dataset of adversarial "misleading" problems; and a large-scale benchmark of 1,000 diverse ODE tasks. The diagnostic set contains problems whose superficial appearance suggests stiffness, and that require algebraic simplification to demonstrate non-stiffness; and the large-scale benchmark spans stiff and non-stiff ODE regimes. We evaluate open- and closed-source LLM models along two axes: (i) unguided versus guided prompting with domain-specific knowledge; and (ii) off-the-shelf versus fine-tuned variants. Our evaluation measures both executability and numerical validity against reference solutions. We find that with sufficient context and guided prompts, newer instruction-following models achieve high accuracy on both criteria. In many cases, recent open-source systems perform strongly without fine-tuning, while older or smaller models still benefit from fine-tuning. Overall, our preliminary results indicate that careful prompting and fine-tuning can yield a specialized LLM agent capable of reliably solving simple ODE problems.

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