cs.AIApr 1, 2026

From Data to Theory: Autonomous Large Language Model Agents for Materials Science

Authors: Samuel Onimpa Alfred, Veera Sundararaghavan

Organizations: Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI 48109

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Abstract

We present an autonomous large language model (LLM) agent for end-to-end, data-driven materials theory development. The model can choose an equation form, generate and run its own code, and test how well the theory matches the data without human intervention. The framework combines step-by-step reasoning with expert-supplied tools, allowing the agent to adjust its approach as needed while keeping a clear record of its decisions. For well-established materials relationships such as the Hall-Petch equation and Paris law, the agent correctly identifies the governing equation and makes reliable predictions on new datasets. For more specialized relationships, such as Kuhn's equation for the HOMO-LUMO gap of conjugated molecules as a function of length, performance depends more strongly on the underlying model, with GPT-5 showing better recovery of the correct equation. Beyond known theories, the agent can also suggest new predictive relationships, illustrated here by a strain-dependent law for changes in the HOMO-LUMO gap. At the same time, the results show that careful validation remains essential, because the agent can still return incorrect, incomplete, or inconsistent equations even when the numerical fit appears strong. Overall, these results highlight both the promise and the current limitations of autonomous LLM agents for AI-assisted scientific modeling and discovery.

Figures & tables

Figure 1: Schematic overview of the three-component autonomous fitting framework, illustrating the closed-loop iterative workflow. The Reasoning Engine, Tool Registry, and Agent State interact through a closed-loop iterative workflow comprising Thought, Action, and Observation steps.
Figure 2: Structured response format . At each iteration, the LLM responds with a Thought , an Action specifying a tool and its input, and an Observation that captures the tool’s output.
Figure 3: Sample tool entry for the generate_function tool .Each tool in the registry is defined by a description, an input schema, and an execution function.
ToolDescriptionInput SchemaPurpose
load_dataLoad experimental data{"filename": "path"}Data ingestion
generate_functionGenerate physical equation from LLM’s knowledge{}Symbolic function generation with no-fallback
fit_modelPerform nonlinear least squares fitting{"initial_params": ...}Parameter optimization
test_functionValidate generated function with sample inputs{"test_params": [values], ...}Prevents invalid functions
validate_fitCalculate goodness-of-fit metrics{}Computes R², RMSE, residuals
create_plotsGenerate visualizations{}Produces diagnostic plots
Table 1: Core tools in the agentic framework. Each tool implements a specific operation required for empirical model fitting.
Figure 4: Sample task-specific system prompt. The LLM is initialized with a prompt that defines its role, the target physical context, and the expected reasoning structure.
Figure 5: Logical substructures of the agent’s state . The state is organized into modular fields that are updated by tool executions.
Figure 6: Agent-generated Hall-Petch fitting results .Experimental data points (blue circles) are shown together with the fitted Hall-Petch line (red line)).
Figure 7: Agent-generated Paris law fitting results. Experimental data points (blue circles) are shown together with the fitted Paris line (red line)).
Figure 8: DFT(LDA) HOMO-LUMO gaps for helicenes as a function of chain length. The solid blue curve represents the fit provided by the GPT-5 powered agent using the Kuhn’s equation.
SourceGPT-4 PoweredGPT-5 Powered
Knowledge recallh28mL2N+V0\displaystyle\frac{h^{2}}{8mL^{2}}N+V_{0}h28mL2(N+1)+V0\displaystyle\frac{h^{2}}{8mL^{2}}(N+1)+V_{0}
Literatureh28mL2(N+1)+V0\displaystyle\frac{h^{2}}{8mL^{2}}(N+1)+V_{0}h28mL2(N+1)+V0(1−1N)\displaystyle\frac{h^{2}}{8mL^{2}}(N+1)+V_{0}\left(1-\frac{1}{N}\right)
Table 2: Equations generated by GPT-4 and GPT-5 powered agents across knowledge recall and literature extraction tasks.
Figure 9: Reasoning trace showing PDF extraction failure and subsequent successful equation extraction from HTML.
Figure 10: Prompt provided to the agent to model strain effects. The LLM is initialized with a prompt that defines its role, the physical context (modifying the Kuhn equation for strain effects), and the expected reasoning-action-observation workflow.
Figure 11: Representative output plot from multiple agent runs showing the strain-modified Kuhn equation predictions.
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