Data-Driven Science and Physically Interpretable Machine Learning for Complex Dynamic Systems

Data-Driven Science and Physically Interpretable Machine Learning for Complex Dynamic Systems

In recent years, data-driven science has revolutionized how we understand and predict complex phenomena—from climate patterns and fluid dynamics to financial markets and biological systems. But as data becomes richer and models more powerful, a critical question emerges: how can we ensure that machine learning doesn’t just predict well, but also explains why?

The Challenge of Complexity

Complex dynamic systems—like turbulent flows, ecosystems, or the human brain—are governed by nonlinear interactions and multiscale feedback loops. Traditional modeling relies on physical laws expressed as differential equations. These approaches provide interpretability but often struggle with high-dimensional data and unknown parameters.

Machine learning (ML), on the other hand, thrives on large datasets and can uncover hidden relationships without explicit physical assumptions. Yet, most ML models are black boxes, offering accuracy without understanding.

Bridging Physics and Machine Learning

The emerging field of physically interpretable machine learning (PIML) aims to bridge this gap. Rather than replacing physics with data, PIML integrates physical constraints, symmetries, and conservation laws into data-driven models.

This fusion offers the best of both worlds:

• 🧠 Interpretability: Models that respect known physics provide transparent reasoning.

• ⚙️ Accuracy: Data-driven corrections capture unknown dynamics or missing physics.

• 🌎 Generalizability: Physics-informed models extrapolate better to unseen conditions.

For example, Physics-Informed Neural Networks (PINNs) embed physical equations into the learning process, allowing the network to infer both observed and hidden dynamics directly from data. Similarly, sparse regression methods like SINDy (Sparse Identification of Nonlinear Dynamics) extract governing equations from data, revealing interpretable models with physical meaning.

Applications Across Disciplines

• Climate and Weather Modeling 🌦️ — Integrating ML with physical climate models improves long-term predictability while maintaining energy balance.

• Engineering Systems ⚙️ — Data-driven surrogates can accelerate simulations of fluid flows or material deformation, enabling real-time control.

• Biological and Ecological Systems 🌿 — Hybrid models uncover causal interactions and predict ecosystem resilience under changing conditions.

• Energy and Sustainability 🔋 — Machine learning guided by thermodynamic principles enhances efficiency in energy networks and chemical processes.

The Future of Data-Driven Discovery

The next decade will see a paradigm shift from purely data-driven modeling toward physics-guided intelligence. Researchers are now focusing on:

• Embedding uncertainty quantification to measure model confidence.

• Developing interpretable architectures like symbolic regression and graph neural networks.

• Building digital twins that integrate real-time data streams with physically grounded simulations.

Ultimately, data-driven science and physically interpretable ML will not only predict complex behaviors but also reveal the governing principles behind them—turning raw data into true scientific understanding.

8th Edition of Scientists  Research Awards | 27-28 October 2025 | Paris, France

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