Algorithmic Discovery of Governing Equations in Complex Dynamical Systems
A New Paradigm for Data-Driven Physics
The discovery of physical laws has historically relied on human intuition to postulate mathematical models, followed by experimental validation. In regimes of high dimensionality and complexity — such as many-body quantum dynamics or multi-target drug discovery — first-principles analytical derivation often becomes impractical.
ActarusLab presents an integrated framework that transforms scientific discovery into a problem of optimized search in function space. Through the use of Symbolic Regression (SR) and Scientific Machine Learning (SciML), we automate the extraction of interpretable governing equations, overcoming the limitations of computational "black boxes".
The transition proposed by ActarusLab is not merely a technical advancement, but an epistemological leap based on three pillars:
We replace the theoretical bias of the observer with rigorous algorithmic exploration. We don't instruct the machine on what to look for; we provide the mathematical grammar so that physical law emerges directly from the data.
Traditional Machine Learning provides opaque statistical predictions. ActarusLab provides Verifiable Symbolic Representations. The output is an explicit equation, the only universal language of science.
We transform stochastic intuition into a deterministic, scalable, and reproducible computational process.
We use advanced simulation engines (QuTiP, Monte Carlo, CFD) to generate synthetic datasets that map the state space of a complex system (150k+ scenarios), defining the boundaries of the domain of applicability.
Through symbolic regression algorithms (PySR) and sparse identification (SINDy), we scan the space of mathematical structures P(Model | Data).
Pareto-Front Optimization: We systematically balance model accuracy with its symbolic complexity, favoring parsimony (Occam's Razor).
We apply rigorous Out-of-Fold (OOF) validation protocols. In our pIC50 prediction study (R²=0.74), we demonstrated that robustness on unseen data is the only parameter of scientific reliability, rejecting benchmarks inflated by structural leakage.
By applying the framework to the long-range Ising model, we extracted the previously unknown dynamical phase boundary:
This demonstrates the machine's ability to identify critical regimes that are analytically inaccessible.
The integration of Graph Attention Networks (GAT) and Gradient Boosting has enabled us to establish new standards of reliability in computational chemistry, drastically reducing the false positive rate in pharmaceutical lead optimization.
ActarusLab offers a "machine that finds physics" to achieve:
The future of science does not lie in abandoning theory in favor of data, but in using data to automatically generate theory. ActarusLab is the catalyst for this transition: we transform noise into laws, and laws into competitive advantage.
Scientific Director: Prof. Igor Merlini
Laboratory: ActarusLab
Email: actaruslab@proton.me