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Physics-informed neural networks approach the approximation of differential equations by directly incorporating their structure and given conditions in a loss function. This enables conditions like, e.g., invariants to be easily added…

We present a differentiable simulation architecture for articulated rigid-body dynamics that enables the augmentation of analytical models with neural networks at any point of the computation. Through gradient-based optimization,…

Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…

Recently, physics informed neural networks have successfully been applied to a broad variety of problems in applied mathematics and engineering. The principle idea is to use a neural network as a global ansatz function to partial…

Quantum annealing is a promising paradigm for building practical quantum computers. Compared to other approaches, quantum annealing technology has been scaled up to a larger number of qubits. On the other hand, deep learning has been…

To improve predictive models for STEM applications, supplemental physics-based features computed from input parameters are introduced into single and multiple layers of a deep neural network (DNN). While many studies focus on informing DNNs…

Many types of physics-informed neural network models have been proposed in recent years as approaches for learning solutions to differential equations. When a particular task requires solving a differential equation at multiple…

Deep neural networks (DNNs) have achieved remarkable empirical success, yet the absence of a principled theoretical foundation continues to hinder their systematic development. In this survey, we present differential equations as a…

Modern machine learning algorithms, especially deep learning based techniques, typically involve careful hyperparameter tuning to achieve the best performance. Despite the surge of intense interest in practical techniques like Bayesian…

Dynamical systems see widespread use in natural sciences like physics, biology, chemistry, as well as engineering disciplines such as circuit analysis, computational fluid dynamics, and control. For simple systems, the differential…

Physics-informed neural networks and operator networks have shown promise for effectively solving equations modeling physical systems. However, these networks can be difficult or impossible to train accurately for some systems of equations.…

Industrial process optimization and control is crucial to increase economic and ecologic efficiency. However, data sovereignty, differing goals, or the required expert knowledge for implementation impede holistic implementation. Further,…

Deep neural networks (DNNs) are powerful machine learning models and have succeeded in various artificial intelligence tasks. Although various architectures and modules for the DNNs have been proposed, selecting and designing the…

Scientific applications increasingly demand real-time surrogate models that can capture the behavior of strongly coupled multiphysics systems driven by multiple input functions, such as in thermo-mechanical and electro-thermal processes.…

Decision making algorithms are used in a multitude of different applications. Conventional approaches for designing decision algorithms employ principled and simplified modelling, based on which one can determine decisions via tractable…

Binary neural networks, i.e., neural networks whose parameters and activations are constrained to only two possible values, offer a compelling avenue for the deployment of deep learning models on energy- and memory-limited devices. However,…

Current physics-informed (standard or deep operator) neural networks still rely on accurately learning the initial and/or boundary conditions of the system of differential equations they are solving. In contrast, standard numerical methods…

Modern buildings encompass complex dynamics of multiple electrical, mechanical, and control systems. One of the biggest hurdles in applying conventional model-based optimization and control methods to building energy management is the huge…

In this paper we consider a distributed optimization scenario in which a set of agents has to solve a convex optimization problem with separable cost function, local constraint sets and a coupling inequality constraint. We propose a novel…

Hyperparameter optimization is both a practical issue and an interesting theoretical problem in training of deep architectures. Despite many recent advances the most commonly used methods almost universally involve training multiple and…