# Transfer Learning with Reduced Order Models for Dynamical Systems How simplified models accelerate reinforcement learning in complex physics simulations. - **Source:** [Towards Data Science](https://towardsdatascience.com) - **Published:** 2026-09-05 - **Topic:** [Data & AI](https://brifing.si/c/data-ai) - **Original article:** - **On Brifing:** https://brifing.si/s/d7b4fc49-3c0d-490a-99a8-e25ecda50ff1 ## The Challenge of RL in Physics Reinforcement Learning (RL) faces major hurdles when applied to complex physical systems due to lengthy training times. Simulating intricate physics like fluid dynamics or thermodynamics can take hours per iteration. Combined with thousands of training cycles needed for nonlinear systems, this creates computationally intractable problems. Traditional approaches struggle with real-world nonlinearities where system responses aren't predictable. ## Transfer Learning Solution Transfer learning offers a solution by leveraging knowledge from similar problems. Just as an RL model trained on RC cars can adapt faster to trucks than starting from scratch, physics simulations can benefit from pre-trained models. The key is finding sufficiently similar environments that simulate faster than original systems. This approach maintains accuracy while dramatically cutting computational costs. ## Reduced Order Models Explained Reduced Order Models (ROMs) are simplified versions that preserve essential dynamics. They act as 'training wheels' for RL algorithms, providing faster simulations that capture core behaviors. Any AI model can serve as a ROM - even language models approximate human communication. For physics, we create data-driven ROMs using only system measurements, requiring minimal prior knowledge of underlying physics. ## Dynamical Systems Complexity Real-world systems like jet engines exhibit nonlinear dynamics where small input changes can cause disproportionate outputs. Traditional analytical methods fail as complexity increases. While we lack comprehensive governing equations, our capacity to collect and process massive datasets (GB to PB scale) has grown exponentially, enabling new data-driven approaches to system modeling. ## SINDy Algorithm Breakthrough Sparse Identification of Nonlinear Dynamics (SINDy) represents a paradigm shift. This unsupervised learning method discovers mathematical models directly from time-series data without predefined equations. It tests candidate equation terms (like derivatives or products) to find the simplest model explaining observed behavior. SINDy has successfully modeled complex fluid flows from data alone. ## How SINDy Works Mathematically The algorithm solves d x /dt = θ(x)Ξ, where θ(x) contains possible equation terms and Ξ is their coefficients. For a quadratic system, quadratic terms get large coefficients while irrelevant terms (like sinusoids) approach zero. This parsimonious approach automatically identifies the minimal model structure needed to capture system dynamics from measurement data. ## Turbojet Engine Case Study Jet engines present extreme modeling challenges with coupled fluid, structural, thermodynamic and chemical processes. Current simulations use iterative solutions of simplified equations. SINDy offers potential to discover more accurate models directly from operational data, possibly revealing previously unknown dynamic relationships in these complex systems. ## Data-Driven Modeling Advantages Traditional physics-based modeling requires extensive domain expertise to derive equations. Data-driven approaches like SINDy can extract models directly from measurements, potentially discovering unexpected relationships. This is particularly valuable for systems where first-principles modeling is impractical or incomplete equations exist. ## Computational Efficiency Gains ROMs combined with transfer learning create an efficient pipeline: 1) SINDy derives ROM from measurement data, 2) RL trains on fast ROM simulations, 3) Knowledge transfers to full-scale model. This can reduce training time from months to days while maintaining sufficient accuracy for control applications. ## Industry Applications Beyond aerospace, these methods apply to any complex physical system: power grids, chemical plants, or biomedical devices. As sensors proliferate in industrial equipment, data-driven modeling becomes increasingly viable. Early adopters in energy and manufacturing are already seeing benefits in predictive maintenance and control optimization. ## Future Research Directions Current limitations include handling very high-dimensional systems and ensuring ROM robustness. Future work may combine SINDy with deep learning for scaling, or develop hybrid models blending data-driven and physics-based approaches. As computational power grows, these methods could revolutionize how we model and control complex real-world systems. ## Transformative Potential This convergence of data science and physics represents a fundamental shift in engineering practice. By combining measurement data with machine learning, we can model systems too complex for traditional analysis. The implications span scientific discovery, industrial optimization, and next-generation control systems - potentially accelerating innovation across multiple engineering disciplines. ## Sources covering this story - https://towardsdatascience.com/dynamical-system-transfer-learning-with-reduced-order-models/ — --- _Summary written by Brifing from the original reporting. Copyright in the original article belongs to its publisher; read the full piece at the link above._