Published June 4, 2026
| Version 2.0.0
Software
Open
Anomaly-Driven Correction Discovery (ADCD): Physics-Constrained Symbolic Regression for Evolutionary Scientific Discovery
Description
This is the official code repository for Anomaly-Driven Correction Discovery (ADCD), a physics-informed symbolic regression framework designed to mimic the evolutionary nature of scientific discovery. Rather than learning entire equations from scratch, ADCD takes a known classical physical law and seeks to discover the mathematical structure of the dimensionless correction term (Δ) that explains the discrepancy between classical predictions and anomalous experimental observations.
Key Features:
- Cascaded Physics Gates: Enforces physical constraints including AST complexity, dimensional homogeneity, transcendental argument guardrails, and asymptotic limits (ARC).
- JAX-Traced Parameter Optimization: Leverages automatic differentiation and JIT-compilation using L-BFGS-B parameter fitting.
- Noise Robustness: Integrates Bayesian Information Criterion (BIC) to prevent overfitting on noisy data up to 10% noise.
- Real Data Infrastructure: Built-in loaders and benchmarks for Mercury orbital precession, Hydrogen Lamb shift, Blackbody radiation, and Muon g-2 anomaly.
Files
ADCD_paper.pdf
Files
(467.2 kB)
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Additional details
Software
- Repository URL
- https://github.com/apiprdt/PhysicsPaper
- Programming language
- Python
- Development Status
- Active
References
- Udrescu, S. M., & Tegmark, M. (2020). AI Feynman: A physics-inspired systematic approach to symbolic regression. Science Advances, 6(16).
- Cranmer, M. (2020). PySR: Fast & parallelized symbolic regression in Python/Julia. arXiv preprint arXiv:2007.03738.
- Schmidt, M., & Lipson, H. (2009). Distilling free-form natural laws from experimental data. Science, 324(5923), 81-85.
- Brunton, S. L., Proctor, J. L., & Kutz, J. N. (2016). Discovering governing equations from data by sparse identification. Proceedings of the National Academy of Sciences, 113(15), 3932-3937.
- Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6(2), 461-464.
- Hornik, K., Stinchcombe, M., & White, H. (1989). Universal approximation of an unknown mapping. Neural Networks, 2(5), 359-366.
- Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2019). Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378, 686-707.
- Greydanus, S., Dzamba, M., & Yosinski, J. (2019). Hamiltonian neural networks. Advances in Neural Information Processing Systems (NeurIPS), 32.
- Cranmer, M., Greydanus, S., Hoyer, S., Battaglia, P., Spergel, D., & Ho, S. (2020). Lagrangian neural networks. ICLR 2020 Deep Differential Equations Workshop.
- Petersen, B. K., et al. (2021). Deep symbolic regression: Recovering mathematical expressions from data via risk-seeking policy gradients. International Conference on Learning Representations (ICLR).
- Kitano, H. (2021). Nobel Turing challenge: creating the engine for scientific discovery. npj Systems Biology and Applications, 7(29).
- Romera-Paredes, B., et al. (2024). Mathematical discoveries from program search with large language models. Nature, 625, 468-475.
- Rissanen, J. (1978). Modeling by shortest data description. Automatica, 14(5), 465-471.
- Langley, P., Simon, H. A., Bradshaw, G. L., & Zytkow, J. M. (1987). Scientific Discovery: Computational Explorations of the Creative Processes. MIT Press.