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Modeling nonlinear spatiotemporal dynamical systems has primarily relied on partial differential equations (PDEs). However, the explicit formulation of PDEs for many underexplored processes, such as climate systems, biochemical reaction and…

In physics, complex systems are often simplified into minimal, solvable models that retain only the core principles. In machine learning, layerwise linear models (e.g., linear neural networks) act as simplified representations of neural…

In systems with detailed balance, the stationary distribution and the equilibrium distribution are identical, creating a clear connection between energetic and entropic quantities. Many driven systems violate detailed balance and still pose…

We introduce Neural Dynamical Systems (NDS), a method of learning dynamical models in various gray-box settings which incorporates prior knowledge in the form of systems of ordinary differential equations. NDS uses neural networks to…

Despite the striking successes of deep neural networks trained with gradient-based optimization, these methods differ fundamentally from their biological counterparts. This gap raises key questions about how nature achieves robust,…

In control design most control strategies are model-based and require accurate models to be applied successfully. Due to simplifications and the model-reality-gap physics-derived models frequently exhibit deviations from real-world-systems.…

We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…

While deep learning has shown tremendous success in a wide range of domains, it remains a grand challenge to incorporate physical principles in a systematic manner to the design, training, and inference of such models. In this paper, we aim…

Physics relies on mathematical spaces carefully matched to the phenomena under study. Phase space in classical mechanics, Hilbert space in quantum theory, configuration spaces in field theory all provide representations in which physical…

Unlike quasi-static robotic manipulation tasks like pick-and-place, dynamic tasks such as non-prehensile manipulation pose greater challenges, especially for vision-based control. Successful control requires the extraction of features…

Model-based methods are the dominant paradigm for controlling robotic systems, though their efficacy depends heavily on the accuracy of the model used. Deep neural networks have been used to learn models of robot dynamics from data, but…

The ability to explain decisions made by machine learning models remains one of the most significant hurdles towards widespread adoption of AI in highly sensitive areas such as medicine, cybersecurity or autonomous driving. Great interest…

In typical machine learning tasks and applications, it is necessary to obtain or create large labeled datasets in order to to achieve high performance. Unfortunately, large labeled datasets are not always available and can be expensive to…

Predicting the future behaviour of complex systems exhibiting critical-like dynamics is often considered to be an intrinsically hard task. Here, we study the predictability of the depinning dynamics of elastic interfaces in random media…

Control of underactuated dynamical systems has been studied for decades in robotics, and is now emerging in other fields such as neuroscience. Most of the advances have been in model based control theory, which has limitations when the…

To achieve virtual certification for industrial design, quantifying the uncertainties in simulation-driven processes is crucial. We discuss a physics-constrained approach to account for epistemic uncertainty of turbulence models. In order…

Accurately predicting fluid dynamics and evolution has been a long-standing challenge in physical sciences. Conventional deep learning methods often rely on the nonlinear modeling capabilities of neural networks to establish mappings…

The goal of Science is to understand phenomena and systems in order to predict their development and gain control over them. In the scientific process of knowledge elaboration, a crucial role is played by models which, in the language of…

The application of learning-based control methods in robotics presents significant challenges. One is that model-free reinforcement learning algorithms use observation data with low sample efficiency. To address this challenge, a prevalent…

Physics-informed neural network architectures have emerged as a powerful tool for developing flexible PDE solvers which easily assimilate data, but face challenges related to the PDE discretization underpinning them. By instead adapting a…