SciML Agents: Write the Solver, Not the Solution
This work addresses the problem of automating scientific computing tasks for researchers and engineers, though it is incremental as it builds on existing LLM capabilities for code generation.
The paper tackles the challenge of using LLMs to generate scientifically appropriate code for solving ODEs, shifting from predicting solutions to making domain-aware numerical choices, and introduces new datasets and benchmarks, finding that guided prompting and fine-tuning enable high accuracy in executability and numerical validity.
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.