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Sequential Bayesian inference over predictive functions is a natural framework for continual learning from streams of data. However, applying it to neural networks has proved challenging in practice. Addressing the drawbacks of existing…

For more than two centuries, solutions of differential equations have been obtained either analytically or numerically based on typically well-behaved forcing and boundary conditions for well-posed problems. We are changing this paradigm in…

Inverse problems, i.e., estimating parameters of physical models from experimental data, are ubiquitous in science and engineering. The Bayesian formulation is the gold standard because it alleviates ill-posedness issues and quantifies…

Bayesian posterior inference is prevalent in various machine learning problems. Variational inference provides one way to approximate the posterior distribution, however its expressive power is limited and so is the accuracy of resulting…

Learning long-term behaviors in chaotic dynamical systems, such as turbulent flows and climate modelling, is challenging due to their inherent instability and unpredictability. These systems exhibit positive Lyapunov exponents, which…

Machine learning is gaining growing momentum in various recent models for the dynamic analysis of information flows in data communications networks. These preliminary models often rely on off-the-shelf learning models to predict from…

This paper presents a machine learning methodology to improve the predictions of traditional RANS turbulence models in channel flows subject to strong variations in their thermophysical properties. The developed formulation contains several…

This paper introduces Bayesian Flow Networks (BFNs), a new class of generative model in which the parameters of a set of independent distributions are modified with Bayesian inference in the light of noisy data samples, then passed as input…

The numerical solution of differential equations using neural networks has become a central topic in scientific computing, with Physics-Informed Neural Networks (PINNs) emerging as a powerful paradigm for both forward and inverse problems.…

Future frame prediction in videos is a promising avenue for unsupervised video representation learning. Video frames are naturally generated by the inherent pixel flows from preceding frames based on the appearance and motion dynamics in…

Deep feedforward neural networks (DFNNs) are a powerful tool for functional approximation. We describe flexible versions of generalized linear and generalized linear mixed models incorporating basis functions formed by a DFNN. The…

Variational principles are a unifying mathematical framework across many areas of physics, yet their instruction at the undergraduate level remains primarily analytical. This work presents a pedagogically oriented and computationally…

Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like Partial Differential Equations (PDE), as a component of the neural network itself. PINNs are nowadays used to solve PDEs, fractional…

Physics-informed neural networks (PINNs) have received significant attention as a unified framework for forward, inverse, and surrogate modeling of problems governed by partial differential equations (PDEs). Training PINNs for forward…

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…

Model discovery aims at autonomously discovering differential equations underlying a dataset. Approaches based on Physics Informed Neural Networks (PINNs) have shown great promise, but a fully-differentiable model which explicitly learns…

Artificial Neural Networks are connectionist systems that perform a given task by learning on examples without having prior knowledge about the task. This is done by finding an optimal point estimate for the weights in every node.…

In this paper, we introduce a modular deep neural network (DNN) framework for data-driven reduced order modeling of dynamical systems relevant to fluid flows. We propose various deep neural network architectures which numerically predict…

A novel hybrid deep neural network architecture is designed to capture the spatial-temporal features of unsteady flows around moving boundaries directly from high-dimensional unsteady flow fields data. The hybrid deep neural network is…

In recent years, Physics-Informed Neural Networks (PINNs) have emerged as a powerful and robust framework for solving nonlinear differential equations across a wide range of scientific and engineering disciplines, including biology,…