Related papers: Learning with Physical Constraints
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…
Engineering design and scientific analysis rely upon computer simulations of turbulent fluid flows using turbulence models. These turbulence models are empirical and approximate, leading to large uncertainties in their predictions that…
We propose a physics-aware Consistency Training (CT) method that accelerates sampling in Diffusion Models with physical constraints. Our approach leverages a two-stage strategy: (1) learning the noise-to-data mapping via CT, and (2)…
We propose a new family of neural networks to predict the behaviors of physical systems by learning their underpinning constraints. A neural projection operator lies at the heart of our approach, composed of a lightweight network with an…
Data-driven algorithms, in particular neural networks, can emulate the effect of sub-grid scale processes in coarse-resolution climate models if trained on high-resolution climate simulations. However, they may violate key physical…
Physics-constrained neural networks are commonly employed to enhance prediction robustness compared to purely data-driven models, achieved through the inclusion of physical constraint losses during the model training process. However, one…
Inspired by applications in optimal control of semilinear elliptic partial differential equations and physics-integrated imaging, differential equation constrained optimization problems with constituents that are only accessible through…
This tutorial paper provides an introduction to recently developed tools for machine learning, especially learning dynamical systems (system identification), with stability and robustness constraints. The main ideas are drawn from…
The problem of ensuring constraints satisfaction on the output of machine learning models is critical for many applications, especially in safety-critical domains. Modern approaches rely on penalty-based methods at training time, which do…
We demonstrate that embedding physics-driven constraints into machine learning process can dramatically improve accuracy and generalizability of the resulting model. Physics-informed learning is illustrated on the example of analysis of…
Reinforcement Learning (RL) agents have great successes in solving tasks with large observation and action spaces from limited feedback. Still, training the agents is data-intensive and there are no guarantees that the learned behavior is…
This document is a hands-on, comprehensive guide to deep learning in the realm of physical simulations. Rather than just theory, we emphasize practical application: every concept is paired with interactive Jupyter notebooks to get you up…
In this work we present deep learning implementations of two popular theoretical constrained optimization algorithms in infinite dimensional Hilbert spaces, namely, the penalty and the augmented Lagrangian methods. We test these algorithms…
Integrating learning-based techniques, especially reinforcement learning, into robotics is promising for solving complex problems in unstructured environments. However, most existing approaches are trained in well-tuned simulators and…
This tutorial paper focuses on safe physics-informed machine learning in the context of dynamics and control, providing a comprehensive overview of how to integrate physical models and safety guarantees. As machine learning techniques…
This paper presents an approach for inferring geometric constraints in human demonstrations. In our method, geometric constraint models are built to create representations of kinematic constraints such as fixed point, axial rotation,…
In Programming by Demonstration, the robot learns novel skills from human demonstrations. After learning, the robot should be able not only to reproduce the skill, but also to generalize it to shifted domains without collecting new training…
We assume that we are given a time series of data from a dynamical system and our task is to learn the flow map of the dynamical system. We present a collection of results on how to enforce constraints coming from the dynamical system in…
In the recent years, deep learning approaches have shown much promise in modeling complex systems in the physical sciences. A major challenge in deep learning of PDEs is enforcing physical constraints and boundary conditions. In this work,…
Neural differential equations offer a powerful approach for learning dynamics from data. However, they do not impose known constraints that should be obeyed by the learned model. It is well-known that enforcing constraints in surrogate…