Related papers: Robust learning from noisy, incomplete, high-dimen…

Dimensionless numbers and scaling laws provide elegant insights into the characteristic properties of physical systems. Classical dimensional analysis and similitude theory fail to identify a set of unique dimensionless numbers for a…

Obtaining system parameters and reconstructing the full flow state from limited velocity observations using conventional fluid dynamics solvers can be prohibitively expensive. Here we employ machine learning algorithms to overcome the…

Reduced-order modelling and system identification can help us figure out the elementary degrees of freedom and the underlying mechanisms from the high-dimensional and nonlinear dynamics of fluid flow. Machine learning has brought new…

In spatially extended systems, it is common to find latent variables that are hard, or even impossible, to measure with acceptable precision, but are crucially important for the proper description of the dynamics. This substantially…

Discovering the underlying dynamics of complex systems from data is an important practical topic. Constrained optimization algorithms are widely utilized and lead to many successes. Yet, such purely data-driven methods may bring about…

The development of data-informed predictive models for dynamical systems is of widespread interest in many disciplines. We present a unifying framework for blending mechanistic and machine-learning approaches to identify dynamical systems…

Data-driven, model-free analytics are natural choices for discovery and forecasting of complex, nonlinear systems. Methods that operate in the system state-space require either an explicit multidimensional state-space, or, one approximated…

Machine learning models are gaining increasing popularity in the domain of fluid dynamics for their potential to accelerate the production of high-fidelity computational fluid dynamics data. However, many recently proposed machine learning…

This paper presents a robust data-driven controller design based on the noisy input-output data without assumptions on the statistical properties of the noises. We start with the direct data-representation of system models that take…

While trade-offs between modeling effort and model accuracy remain a major concern with system identification, resorting to data-driven methods often leads to a complete disregard for physical plausibility. To address this issue, we propose…

This study presents a physics-informed machine learning-based control method for nonlinear dynamic systems with highly noisy measurements. Existing data-driven control methods that use machine learning for system identification cannot…

In many applications, flow measurements are usually sparse and possibly noisy. The reconstruction of a high-resolution flow field from limited and imperfect flow information is significant yet challenging. In this work, we propose an…

Discovery of new natural laws has for a long time relied on the inspiration of some genius. Recently, however, machine learning technologies, which analyze big data without human prejudice and bias, are expected to find novel natural laws.…

Modeling real-world systems requires accounting for noise - whether it arises from unpredictable fluctuations in financial markets, irregular rhythms in biological systems, or environmental variability in ecosystems. While the behavior of…

Machine learning has become a powerful tool for discovering governing laws of dynamical systems from data. However, most existing approaches degrade severely when observations are sparse, noisy, or irregularly sampled. In this work, we…

Many real-world systems can be described by mathematical models that are human-comprehensible, easy to analyze and help explain the system's behavior. Symbolic regression is a method that can automatically generate such models from data.…

Dimensionless learning is a data-driven framework for discovering dimensionless numbers and scaling laws from experimental measurements. This tutorial introduces the method, explaining how it transforms experimental data into compact…

Throughout the history of science, physics-based modeling has relied on judiciously approximating observed dynamics as a balance between a few dominant processes. However, this traditional approach is mathematically cumbersome and only…

The ability to discover physical laws and governing equations from data is one of humankind's greatest intellectual achievements. A quantitative understanding of dynamic constraints and balances in nature has facilitated rapid development…

We show how a complete mathematical description of a complicated physical phenomenon can be learned from observational data via a hybrid approach combining three simple and general ingredients: physical assumptions of smoothness, locality,…