Related papers: Discretization-independent multifidelity operator …

The multiscale complexity of modern problems in computational science and engineering can prohibit the use of traditional numerical methods in multi-dimensional simulations. Therefore, novel algorithms are required in these situations to…

Learning discrete representations of data is a central machine learning task because of the compactness of the representations and ease of interpretation. The task includes clustering and hash learning as special cases. Deep neural networks…

In recent years, multicalibration has emerged as a desirable learning objective for ensuring that a predictor is calibrated across a rich collection of overlapping subpopulations. Existing approaches typically achieve multicalibration by…

It is important to develop mathematically tractable models than can interpret knowledge extracted from the data and provide reasonable predictions. In this paper, we present a Linear Distillation Learning, a simple remedy to improve the…

Machine unlearning, the process of selectively removing data from trained models, is increasingly crucial for addressing privacy concerns and knowledge gaps post-deployment. Despite this importance, existing approaches are often heuristic…

Dataset distillation (DD) is an increasingly important technique that focuses on constructing a synthetic dataset capable of capturing the core information in training data to achieve comparable performance in models trained on the latter.…

Foundation models, such as large language models, have demonstrated success in addressing various language and image processing tasks. In this work, we introduce a multi-modal foundation model for scientific problems, named PROSE-PDE. Our…

Quantum algorithms for partial differential equations (PDEs) face severe practical constraints on near-term hardware: limited qubit counts restrict spatial resolution to coarse grids, while circuit depth limitations prevent accurate…

It is known that neural networks have the problem of being over-confident when directly using the output label distribution to generate uncertainty measures. Existing methods mainly resolve this issue by retraining the entire model to…

We show that the error achievable using physics-informed neural networks for solving systems of differential equations can be substantially reduced when these networks are trained using meta-learned optimization methods rather than to using…

Deterministic neural nets have been shown to learn effective predictors on a wide range of machine learning problems. However, as the standard approach is to train the network to minimize a prediction loss, the resultant model remains…

Adversarial examples are perturbed inputs that are designed (from a deep learning network's (DLN) parameter gradients) to mislead the DLN during test time. Intuitively, constraining the dimensionality of inputs or parameters of a network…

Image BERT pre-training with masked image modeling (MIM) becomes a popular practice to cope with self-supervised representation learning. A seminal work, BEiT, casts MIM as a classification task with a visual vocabulary, tokenizing the…

Deep neural networks (DNNs) have recently emerged as effective tools for approximating solution operators of partial differential equations (PDEs) including evolutionary problems. Classical numerical solvers for such PDEs often face…

Imitation learning is a widely used approach for training agents to replicate expert behavior in complex decision-making tasks. However, existing methods often struggle with compounding errors and limited generalization, due to the inherent…

In order to both learn and protect sensitive training data, there has been a growing interest in privacy preserving machine learning methods. Differential privacy has emerged as an important measure of privacy. We are interested in the…

We establish a discrete operator--theoretic framework for the analysis of implicit Euler and Lie--Trotter splitting schemes for delay differential equations (DDEs). Both schemes are formulated in terms of discrete resolvent operators acting…

We investigate an approach for the numerical solution of differential equations which is based on the perfect discretization of actions. Such perfect discretizations show up at the fixed points of renormalization group transformations. This…

Neural operators provide a framework for learning solution operators of partial differential equations (PDEs), enabling efficient surrogate modeling for complex systems. While universal approximation results are now well understood,…

Recent advances in scientific machine learning (SciML) have enabled neural operators (NOs) to serve as powerful surrogates for modeling the dynamic evolution of physical systems governed by partial differential equations (PDEs). While…