Related papers: Simulation free reliability analysis: A physics-in…

Learning the optimized solution as a function of environmental parameters is effective in solving numerical optimization in real time for time-sensitive applications. Existing works of learning to optimize train deep neural networks (DNN)…

We revisit empirical Bayes in the absence of a tractable likelihood function, as is typical in scientific domains relying on computer simulations. We investigate how the empirical Bayesian can make use of neural density estimators first to…

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…

Finding self-similarity is a key step for understanding the governing law behind complex physical phenomena. Traditional methods for identifying self-similarity often rely on specific models, which can introduce significant bias. In this…

We introduce a method for training exactly conservative physics-informed neural networks and physics-informed deep operator networks for dynamical systems. The method employs a projection-based technique that maps a candidate solution…

Deep learning algorithms have recently shown to be a successful tool in estimating parameters of statistical models for which simulation is easy, but likelihood computation is challenging. But the success of these approaches depends on…

The numerical approximation of solutions to the compressible Euler and Navier-Stokes equations is a crucial but challenging task with relevance in various fields of science and engineering. Recently, methods from deep learning have been…

Physics-based deep learning frameworks have shown to be effective in accurately modeling the dynamics of complex physical systems with generalization capability across problem inputs. Data-driven networks like GNN, Neural Operators have…

Likelihood-free inference refers to inference when a likelihood function cannot be explicitly evaluated, which is often the case for models based on simulators. Most of the literature is based on sample-based `Approximate Bayesian…

Recent model-free reinforcement learning algorithms have proposed incorporating learned dynamics models as a source of additional data with the intention of reducing sample complexity. Such methods hold the promise of incorporating imagined…

Differential equations are used to model and predict the behaviour of complex systems in a wide range of fields, and the ability to solve them is an important asset for understanding and predicting the behaviour of these systems.…

Physics models typically contain adjustable parameters to reproduce measured data. While some parameters correspond directly to measured features in the data, others are unobservable. These unobservables can, in some cases, cause…

Random cost simulations were introduced as a method to investigate optimization problems in systems with conflicting constraints. Here I study the approach in connection with the training of a feed-forward multilayer perceptron, as used in…

A central challenge in many areas of science and engineering is to identify model parameters that are consistent with prior knowledge and empirical data. Bayesian inference offers a principled framework for this task, but can be…

We present a model-free data-driven inference method that enables inferences on system outcomes to be derived directly from empirical data without the need for intervening modeling of any type, be it modeling of a material law or modeling…

Safety and stability are common requirements for robotic control systems; however, designing safe, stable controllers remains difficult for nonlinear and uncertain models. We develop a model-based learning approach to synthesize robust…

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.…

We demonstrate that challenging shortest path problems can be solved via direct spline regression from a neural network, trained in an unsupervised manner (i.e. without requiring ground truth optimal paths for training). To achieve this, we…

Constructing first-principles models is usually a challenging and time-consuming task due to the complexity of the real-life processes. On the other hand, data-driven modeling, and in particular neural network models often suffer from…

We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations. In this second…