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This work proposes a Stochastic Variational Deep Kernel Learning method for the data-driven discovery of low-dimensional dynamical models from high-dimensional noisy data. The framework is composed of an encoder that compresses…

Discovering governing equations from data, in particular high dimensional data, is challenging in various fields of science and engineering, and it has potential to revolutionise the science and technology in this big data era. This paper…

Machine learning approaches informed by physics have offered new insights into the discovery of constitutive models from data, helping overcome some limitations of traditional constitutive modelling while reducing the cost of otherwise…

We develop a methodology to construct low-dimensional predictive models from data sets representing essentially nonlinear (or non-linearizable) dynamical systems with a hyperbolic linear part that are subject to external forcing with…

Partial differential equations (PDEs) that fit scientific data can represent physical laws with explainable mechanisms for various mathematically-oriented subjects, such as physics and finance. The data-driven discovery of PDEs from…

This review examined the current advancements in data-driven methods for analyzing flow and transport in porous media, which has various applications in energy, chemical engineering, environmental science, and beyond. Although there has…

Model-free data-driven computational mechanics replaces phenomenological constitutive functions by numerical simulations based on data sets of representative samples in stress-strain space. The distance of strain and stress pairs from the…

Discovering interpretable physical laws from high-dimensional data is a fundamental challenge in scientific research. Traditional methods, such as symbolic regression, often produce complex, unphysical formulas when searching a vast space…

Given a finite and noisy dataset generated with a closed-form mathematical model, when is it possible to learn the true generating model from the data alone? This is the question we investigate here. We show that this model-learning problem…

Generative models have gained popularity for their potential applications in imaging science, such as image reconstruction, posterior sampling and data sharing. Flow-based generative models are particularly attractive due to their ability…

This article introduces a new data-driven approach that leverages a manifold embedding generated by the invertible neural network to improve the robustness, efficiency, and accuracy of the constitutive-law-free simulations with limited…

Accurate models of mechanical system dynamics are often critical for model-based control and reinforcement learning. Fully data-driven dynamics models promise to ease the process of modeling and analysis, but require considerable amounts of…

An extendable, efficient and explainable Machine Learning approach is proposed to represent cyclic plasticity and replace conventional material models based on the Radial Return Mapping algorithm. High accuracy and stability by means of a…

Physics-based and data-driven models for remaining useful lifetime (RUL) prediction typically suffer from two major challenges that limit their applicability to complex real-world domains: (1) incompleteness of physics-based models and (2)…

This paper addresses the problem of learning linear dynamical systems from noisy observations. In this setting, existing algorithms either yield biased parameter estimates or have large sample complexities. We resolve these issues by…

The formulation of rheological constitutive equations -- models that relate internal stresses and deformations in complex fluids -- is a critical step in the engineering of systems involving soft materials. While data-driven models provide…

Real-world robotic applications, from autonomous exploration to assistive technologies, require adaptive, interpretable, and data-efficient learning paradigms. While deep learning architectures and foundation models have driven significant…

Turbulent flow over permeable interface is omnipresent featuring complex flow topology. In this work, a data driven, end to end machine learning model has been developed to model the turbulent flow in porous media. For the same, we have…

The dynamics of biological systems, from proteins to cells to organisms, is complex and stochastic. To decipher their physical laws, we need to bridge between experimental observations and theoretical modeling. Thanks to progress in…

Autonomous robots require high degrees of cognitive and motoric intelligence to come into our everyday life. In non-structured environments and in the presence of uncertainties, such degrees of intelligence are not easy to obtain.…