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Learning a privacy-preserving model from sensitive data which are distributed across multiple devices is an increasingly important problem. The problem is often formulated in the federated learning context, with the aim of learning a single…

It is a common practice in the machine learning community to assume that the observed data are noise-free in the input attributes. Nevertheless, scenarios with input noise are common in real problems, as measurements are never perfectly…

We propose a simple method that combines neural networks and Gaussian processes. The proposed method can estimate the uncertainty of outputs and flexibly adjust target functions where training data exist, which are advantages of Gaussian…

Physics Informed Neural Networks is a numerical method which uses neural networks to approximate solutions of partial differential equations. It has received a lot of attention and is currently used in numerous physical and engineering…

This paper presents a general approach to linear stochastic processes driven by various random noises. Mathematically, such processes are described by linear stochastic differential equations of arbitrary order (the simplest non-trivial…

Repeated use of a data sample via adaptively chosen queries can rapidly lead to overfitting, wherein the empirical evaluation of queries on the sample significantly deviates from their mean with respect to the underlying data distribution.…

Deriving governing equations in Electromagnetic (EM) environment based on first principles can be quite tough when there are some unknown sources of noise and other uncertainties in the system. For nonlinear multiple-physics electromagnetic…

One of the pivotal tasks in scientific machine learning is to represent underlying dynamical systems from time series data. Many methods for such dynamics learning explicitly require the derivatives of state data, which are not directly…

Data assimilation, consisting in the combination of a dynamical model with a set of noisy and incomplete observations in order to infer the state of a system over time, involves uncertainty in most settings. Building upon an existing…

The composition of multiple Gaussian Processes as a Deep Gaussian Process (DGP) enables a deep probabilistic nonparametric approach to flexibly tackle complex machine learning problems with sound quantification of uncertainty. Existing…

We present a computationally efficient algorithm for stable numerical differentiation from noisy, uniformly-sampled data on a bounded interval. The method combines multi-interval Fourier extension approximations with an adaptive domain…

Eliciting a high-dimensional probability distribution from an expert via noisy judgments is notoriously challenging, yet useful for many applications, such as prior elicitation and reward modeling. We introduce a method for eliciting the…

Neural networks have proven successful at learning from complex data distributions by acting as universal function approximators. However, they are often overconfident in their predictions, which leads to inaccurate and miscalibrated…

Performative prediction is an emerging paradigm in machine learning that addresses scenarios where the model's prediction may induce a shift in the distribution of the data it aims to predict. Current works in this field often rely on…

Diffusion models have been recently studied as powerful generative inverse problem solvers, owing to their high quality reconstructions and the ease of combining existing iterative solvers. However, most works focus on solving simple linear…

A long-standing problem at the interface of artificial intelligence and applied mathematics is to devise an algorithm capable of achieving human level or even superhuman proficiency in transforming observed data into predictive mathematical…

Noise in data appears to be inevitable in most real-world machine learning applications and would cause severe overfitting problems. Not only can data features contain noise, but labels are also prone to be noisy due to human input. In this…

We present a novel class of Physics-Informed Neural Networks that is formulated based on the principles of Evidential Deep Learning, where the model incorporates uncertainty quantification by learning parameters of a higher-order…

Bayesian deep learning approaches assume model parameters to be latent random variables and infer posterior distributions to quantify uncertainty, increase safety and trust, and prevent overconfident and unpredictable behavior. However,…

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…