AgenticSciML: Collaborative Multi-Agent Systems for Emergent Discovery in Scientific Machine Learning

TL;DR

The paper presents AgenticSciML, a collaborative multi-agent framework that orchestrates 10+ specialized agents to design, critique, and refine SciML models through structured debate, retrieval-augmented memory, and ensemble-guided evolution. It demonstrates emergent modeling strategies across PDE-constrained learning, neural operators, and inverse problems, achieving up to four orders of magnitude error reduction over single-agent baselines and human-designed approaches. Notable contributions include adaptive mixture-of-experts PINNs, decomposition-based PINNs, physics-informed operator learning architectures, and derivative-enhanced training schemes, illustrating forms of model design not explicitly present in the knowledge base. The work suggests a scalable, transparent pathway for autonomous discovery in scientific computing while acknowledging limitations in KB grounding, computational cost, and the need for stronger physics-grounded verification.

Abstract

Scientific Machine Learning (SciML) integrates data-driven inference with physical modeling to solve complex problems in science and engineering. However, the design of SciML architectures, loss formulations, and training strategies remains an expert-driven research process, requiring extensive experimentation and problem-specific insights. Here we introduce AgenticSciML, a collaborative multi-agent system in which over 10 specialized AI agents collaborate to propose, critique, and refine SciML solutions through structured reasoning and iterative evolution. The framework integrates structured debate, retrieval-augmented method memory, and ensemble-guided evolutionary search, enabling the agents to generate and assess new hypotheses about architectures and optimization procedures. Across physics-informed learning and operator learning tasks, the framework discovers solution methods that outperform single-agent and human-designed baselines by up to four orders of magnitude in error reduction. The agents produce novel strategies -- including adaptive mixture-of-expert architectures, decomposition-based PINNs, and physics-informed operator learning models -- that do not appear explicitly in the curated knowledge base. These results show that collaborative reasoning among AI agents can yield emergent methodological innovation, suggesting a path toward scalable, transparent, and autonomous discovery in scientific computing.

Figures (29)

• Figure 1: Framework for the evolutionary multi-agent SciML system. Phase 1: A Human user provides inputs including problem, requirements, evaluation criteria, and data. Phase 2: Agents analyze user inputs and define solution evaluation criteria, with human approval. Phase 3: Specialized agents (Knowledge Retrievers, Proposers, Critics, Engineers, and Debuggers) collaboratively propose, implement, and execute new solutions. The Result Analyst agent evaluates each solution, which then becomes eligible for mutation in the next iteration.
• Figure 2: Example showing the selection mechanism for solution tree expansion. The best performing solution on the tree is always selected for mutation in the next iteration (exploitation). Additional solutions are selected based on multi-agent majority voting (exploration). This balances the search between refining the best-known solution and exploring alternative approaches that are deemed promising by the agent ensemble. All selections and mutations are performed in parallel.
• Figure 3: Performance improvements achieved by the multi-agent system over single-agent baselines across all benchmark problems. The y-axis shows the improvement factor (root score / champion score) on a logarithmic scale. In every case, the multi-agent system discovers solutions that outperform the single-agent baseline, with improvement factors ranging from 10$\times$ to over 11,000$\times$.
• Figure 4: Ensemble voting agreement across all experiments for top 3 selections. The selectors consistently agree on the first choice and mostly on the second, while the third choice shows disagreement, since different selector agents have different opinions on which solutions have the most potential for improvement.
• Figure 5: Agent contribution analysis across all experiments by word count. The proposer contributes the most, while the user's contribution is minimal.