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Bayesian inference promises to ground and improve the performance of deep neural networks. It promises to be robust to overfitting, to simplify the training procedure and the space of hyperparameters, and to provide a calibrated measure of…
Incorporating a priori physics knowledge into machine learning leads to more robust and interpretable algorithms. In this work, we combine deep learning techniques and classic numerical methods for differential equations to address two…
We present two novel hyperparameter optimization strategies for optimization of deep learning models with a modular architecture constructed of multiple subnetworks. As complex networks with multiple subnetworks become more frequently…
This paper describes a study based on computational fluid dynamics (CFD) and deep neural networks that focusing on predicting the flow field in differently distorted U-shaped pipes. The main motivation of this work was to get an insight…
In lattice quantum field theory studies, parameters defining the lattice theory must be tuned toward criticality to access continuum physics. Commonly used Markov chain Monte Carlo (MCMC) methods suffer from critical slowing down in this…
Deep neural networks are increasingly being used for the analysis of medical images. However, most works neglect the uncertainty in the model's prediction. We propose an uncertainty-aware deep kernel learning model which permits the…
Fluid data completion is a research problem with high potential benefit for both experimental and computational fluid dynamics. An effective fluid data completion method reduces the required number of sensors in a fluid dynamics experiment,…
Modeling the traffic dynamics is essential for understanding and predicting the traffic spatiotemporal evolution. However, deriving the partial differential equation (PDE) models that capture these dynamics is challenging due to their…
This work aims to improve fuel chamber injectors' performance in turbofan engines, thus implying improved performance and reduction of pollutants. This requires the development of models that allow real-time prediction and improvement of…
Neural operators are a type of deep architecture that learns to solve (i.e. learns the nonlinear solution operator of) partial differential equations (PDEs). The current state of the art for these models does not provide explicit…
Deep learning models, such as convolutional neural networks, have long been applied to image and multi-media tasks, particularly those with structured data. More recently, there has been more attention to unstructured data that can be…
Diffusion Monte Carlo (DMC) is one of the most accurate techniques available for calculating the electronic properties of molecules and materials, yet it often remains a challenge to economically compute forces using this technique. As a…
Neural networks are a commonly used approach to replace physical models with computationally cheap surrogates. Parametric uncertainty quantification can be included in training, assuming that an accurate prior distribution of the model…
Computing accurate yet efficient approximations to the solutions of the electronic Schr\"odinger equation has been a paramount challenge of computational chemistry for decades. Quantum Monte Carlo methods are a promising avenue of…
Gaussian processes allow for flexible specification of prior assumptions of unknown dynamics in state space models. We present a procedure for efficient Bayesian learning in Gaussian process state space models, where the representation is…
In this paper we propose a parallel coordinate descent algorithm for solving smooth convex optimization problems with separable constraints that may arise e.g. in distributed model predictive control (MPC) for linear network systems. Our…
In this paper, we consider the problem of learning prediction models for spatiotemporal physical processes driven by unknown partial differential equations (PDEs). We propose a deep learning framework that learns the underlying dynamics and…
Learning-based control aims to construct models of a system to use for planning or trajectory optimization, e.g. in model-based reinforcement learning. In order to obtain guarantees of safety in this context, uncertainty must be accurately…
Deep learning optimization exhibits structure that is not captured by worst-case gradient bounds. Empirically, gradients along training trajectories are often temporally predictable and evolve within a low-dimensional subspace. In this work…
3D microscopy is key in the investigation of diverse biological systems, and the ever increasing availability of large datasets demands automatic cell identification methods that not only are accurate, but also can imply the uncertainty in…