Related papers: Physics-Informed Machine Learning of Dynamical Sys…
Physics-Informed Neural Networks (PINNs) offer a promising approach to solving differential equations and, more generally, to applying deep learning to problems in the physical sciences. We adopt a recently developed transfer learning…
Physics-informed deep learning models have emerged as powerful tools for learning dynamical systems. These models directly encode physical principles into network architectures. However, systematic benchmarking of these approaches across…
Currently, it is hard to reap the benefits of deep learning for Bayesian methods, which allow the explicit specification of prior knowledge and accurately capture model uncertainty. We present Prior-Data Fitted Networks (PFNs). PFNs…
Active learning methods for neural networks are usually based on greedy criteria which ultimately give a single new design point for the evaluation. Such an approach requires either some heuristics to sample a batch of design points at one…
We propose a new class of Bayesian neural networks (BNNs) that can be trained using noisy data of variable fidelity, and we apply them to learn function approximations as well as to solve inverse problems based on partial differential…
Deep neural networks (DNNs) have made a revolution in numerous fields during the last decade. However, in tasks with high safety requirements, such as medical or autonomous driving applications, providing an assessment of the models…
Obtaining heteroscedastic predictive uncertainties from a Bayesian Neural Network (BNN) is vital to many applications. Often, heteroscedastic aleatoric uncertainties are learned as outputs of the BNN in addition to the predictive means,…
Dynamic structural equation modeling (DSEM) is widely used for analyzing intensive longitudinal data (ILD). Although many ILD have categorical (Bernoulli or binomially distributed) responses, currently available Metropolis-within-Gibbs…
Recurrent neural networks (RNNs) are widely used in computational neuroscience and machine learning applications. In an RNN, each neuron computes its output as a nonlinear function of its integrated input. While the importance of RNNs,…
This paper investigates two prominent probabilistic neural modeling paradigms: Bayesian Neural Networks (BNNs) and Mixture Density Networks (MDNs) for uncertainty-aware nonlinear regression. While BNNs incorporate epistemic uncertainty by…
Bayesian networks (BNs) are a widely used graphical model in machine learning for representing knowledge with uncertainty. The mainstream BN structure learning methods require performing a large number of conditional independence (CI)…
Bayesian neural networks (BNNs) have recently regained a significant amount of attention in the deep learning community due to the development of scalable approximate Bayesian inference techniques. There are several advantages of using a…
Recently, Neural Ordinary Differential Equations has emerged as a powerful framework for modeling physical simulations without explicitly defining the ODEs governing the system, but instead learning them via machine learning. However, the…
Machine learning frameworks for physical problems must capture and enforce physical constraints that preserve the structure of dynamical systems. Many existing approaches achieve this by integrating physical operators into neural networks.…
Bayesian Neural Networks (BNNs) have been proposed to address the problem of model uncertainty in training and inference. By introducing weights associated with conditioned probability distributions, BNNs are capable of resolving the…
Neural networks that synergistically integrate data and physical laws offer great promise in modeling dynamical systems. However, iterative gradient-based optimization of network parameters is often computationally expensive and suffers…
In this paper we present a novel implementation of Bayesian CMB component separation. We sample from the full posterior distribution using the No-U-Turn Sampler (NUTS), a gradient-based sampling algorithm. Alongside this, we introduce new…
Bayesian Neural Networks (BNNs) that possess a property of uncertainty estimation have been increasingly adopted in a wide range of safety-critical AI applications which demand reliable and robust decision making, e.g., self-driving, rescue…
A significant advancement in Neural Network (NN) research is the integration of domain-specific knowledge through custom loss functions. This approach addresses a crucial challenge: how can models utilize physics or mathematical principles…
Deep neural networks (DNNs) have become ubiquitous thanks to their remarkable ability to model complex patterns across various domains such as computer vision, speech recognition, robotics, etc. While large DNN models are often more…