Automated Algorithmic Discovery for Scientific Computing through LLM-Guided Evolutionary Search: A Case Study in Gravitational-Wave Detection

Highlights

• Breakthrough in Automated Algorithm Discovery: Evo-MCTS represents a paradigm shift in scientific computing by enabling automated discovery of interpretable algorithms that match or exceed human-designed solutions.

• Exceptional Performance Gains: Achieves 20.2% improvement over domain-specific methods and 59.1% improvement over LLM-based optimization frameworks in gravitational wave detection tasks.

• Interpretability-First Design: Unlike black-box optimization approaches, Evo-MCTS produces transparent, scientifically validatable algorithmic structures that domain experts can understand, verify, and trust.

• Domain-Agnostic Framework: The architecture is designed for generalizability across scientific computing domains, not limited to gravitational wave physics.

• Integration of LLM and Evolutionary Search: Successfully combines the domain knowledge of large language models with the systematic exploration capabilities of Monte Carlo Tree Search.

• Handles Complex Constraints: Effectively manages vast design spaces with expensive evaluations while respecting domain-specific physical constraints requiring expert knowledge.

Key Contributions

1. Novel Framework Architecture

The Evo-MCTS framework introduces a three-pillar approach to automated algorithm discovery:

• Reflective Code Synthesis: Leverages LLM capabilities to generate physically-grounded candidate algorithms informed by domain knowledge
• Multi-Scale Evolutionary Operations: Applies structured mutations on code representations across different abstraction levels, enabling both fine-grained and architectural-level improvements
• Tree-Guided Exploration: Employs Monte Carlo Tree Search to navigate the algorithmic design space systematically, balancing exploration and exploitation

2. Interpretable Algorithm Discovery

Addresses the fundamental challenge in scientific computing where algorithmic transparency is as critical as performance. The framework produces solutions that:

• Integrate multiple functional components coherently
• Emerge from tree-guided exploration as interpretable pathways
• Enable scientists to validate and understand the underlying logic
• Support scientific reproducibility and trust

3. Rigorous Validation in Complex Domain

Demonstrates effectiveness in gravitational wave detection, a particularly challenging domain featuring:

• Continuous high-dimensional parameter spaces
• Strict physical constraints
• Expensive computational evaluations
• Need for domain expert validation

Methodology

Problem Formulation

Automated algorithm discovery in scientific computing faces three fundamental challenges:

1. Vast Design Spaces: Exponential growth of possible algorithmic configurations with expensive evaluation costs
2. Domain Constraints: Physical laws and domain-specific requirements that must be respected
3. Interpretability Requirements: Solutions must be understandable and validatable by scientists

Evo-MCTS Architecture

The framework operates through iterative cycles:

Phase 1: Tree-Guided Exploration

• Monte Carlo Tree Search maintains a tree of algorithmic candidates
• Each node represents a code structure with associated performance metrics
• Selection balances between exploiting promising branches and exploring new regions

Phase 2: LLM-Informed Code Generation

• Large language models generate code variations informed by domain knowledge
• Reflective synthesis ensures physical validity and adherence to constraints
• Multiple scales of mutation enable both refinement and radical redesign

Phase 3: Evolutionary Operations

• Structured mutations on code abstract syntax trees
• Crossover operations between high-performing candidates
• Multi-scale modifications from token-level to block-level changes

Phase 4: Evaluation and Selection

• Candidate algorithms evaluated on realistic benchmark problems
• Performance metrics combined with interpretability scores
• Successful candidates inform future exploration

Key Technical Innovations

• Structured Code Representation: Algorithms represented as abstract syntax trees enabling meaningful mutations
• Domain Knowledge Integration: LLM provides physics-aware code generation rather than blind search
• Interpretable Pathways: Tree structure naturally provides explanation of algorithmic evolution
• Adaptive Exploration: MCTS automatically adjusts exploration strategy based on discovered patterns

Results

Gravitational Wave Detection Performance

The framework was evaluated on gravitational wave detection pipelines, comparing against:

• Domain-specific baseline methods (traditional matched filtering and coherent analysis)
• LLM-based optimization frameworks (pure prompt-based approaches)

Quantitative Improvements:

• 20.2% performance gain over carefully engineered domain-specific methods
• 59.1% performance gain over alternative LLM-based optimization approaches
• Consistent convergence toward high-quality solutions across multiple runs

Algorithm Interpretability

Discovered algorithms exhibit:

• Clear modular structure with identifiable functional components
• Integration of multiple signal processing techniques (filtering, coherent analysis, statistical tests)
• Transparent decision-making logic that domain experts can validate
• Novel combinations of known techniques that were not obvious a priori

Convergence Characteristics

• Efficient exploration of design space with fewer evaluations than baseline evolutionary approaches
• Stable convergence patterns demonstrating robustness
• Ability to escape local optima through LLM-guided exploration

Generalization Capabilities

Although demonstrated on gravitational waves, the domain-agnostic architecture suggests applicability to:

• Other physics simulations requiring custom algorithmic pipelines
• Scientific data analysis problems with complex constraints
• Optimization problems requiring interpretable solutions

Impact

For Gravitational Wave Astronomy

• Accelerated Method Development: Reduces the human time required to design new analysis algorithms from months to days
• Novel Algorithm Discovery: Found effective combinations of techniques not previously considered by domain experts
• Democratization: Makes advanced algorithm design accessible to researchers without deep algorithmic expertise

For Scientific Computing Broadly

• New Paradigm: Establishes automated algorithm discovery as a viable approach for scientific problems
• Interpretability Standards: Demonstrates that performance and transparency need not be competing objectives
• Methodological Framework: Provides a reusable architecture applicable across scientific domains

For AI and Optimization

• LLM Integration: Shows effective ways to incorporate language model capabilities in optimization frameworks
• Hybrid Approaches: Validates combining symbolic methods (tree search) with neural approaches (LLMs)
• Practical Validation: Demonstrates real-world impact beyond benchmark problems

Resources

Code and Implementation

• GitHub Repository: https://github.com/iphysresearch/evo-mcts - Full implementation with examples and documentation
• Project Website: https://iphysresearch.github.io/evo-mcts/ - Comprehensive project documentation, tutorials, and results

Publication and Presentation

• arXiv Paper: arXiv:2508.03661 [cs.AI] - Full technical paper with detailed methodology and experiments
• Presentation Slides: Nature Conference Talk (October 2025) - Overview presentation with key results

Related Work

• LIGO Scientific Collaboration: https://www.ligo.org - Context for gravitational wave detection
• Monte Carlo Tree Search: Classic AI planning method adapted for algorithmic search
• Large Language Models for Code: Building on recent advances in LLM code generation capabilities

Future Directions

The Evo-MCTS framework opens several promising research directions:

• Extension to other scientific computing domains (climate modeling, molecular dynamics, computational chemistry)
• Integration with formal verification tools for stronger correctness guarantees
• Multi-objective optimization balancing performance, interpretability, and computational cost
• Interactive mode allowing human experts to guide the search process
• Automated hyperparameter tuning within discovered algorithms