Related papers: Goal-oriented Uncertainty Quantification for Inver…

These lecture notes highlight the mathematical and computational structure relating to the formulation of, and development of algorithms for, the Bayesian approach to inverse problems in differential equations. This approach is fundamental…

The vector quantization is a widely used method to map continuous representation to discrete space and has important application in tokenization for generative mode, bottlenecking information and many other tasks in machine learning. Vector…

This work addresses data-driven inverse optimization (IO), where the goal is to estimate unknown parameters in an optimization model from observed decisions that can be assumed to be optimal or near-optimal solutions to the optimization…

Deep neural network controllers for autonomous driving have recently benefited from significant performance improvements, and have begun deployment in the real world. Prior to their widespread adoption, safety guarantees are needed on the…

Inverse medium scattering solvers generally reconstruct a single solution without an associated measure of uncertainty. This is true both for the classical iterative solvers and for the emerging deep learning methods. But ill-posedness and…

Recent convolutional neural network (CNN) development continues to advance the state-of-the-art model accuracy for various applications. However, the enhanced accuracy comes at the cost of substantial memory bandwidth and storage…

We combine vision transformers with operator learning to solve diverse inverse problems described by partial differential equations (PDEs). Our approach, named ViTO, combines a U-Net based architecture with a vision transformer. We apply…

Escalating cyber threats and the high-dimensional complexity of IoT traffic have outpaced classical anomaly detection methods. While deep learning offers improvements, computational bottlenecks limit real-time deployment at scale. We…

Deep neural networks (DNNs) have achieved tremendous success in computer vision, natural language processing, and scientific and engineering domains. However, DNNs can make unexpected, incorrect, yet overconfident predictions, leading to…

Anomalies are by definition rare, thus labeled examples are very limited or nonexistent, and likely do not cover unforeseen scenarios. Unsupervised learning methods that don't necessarily encounter anomalies in training would be immensely…

Safe deployment of graph neural networks (GNNs) under distribution shift requires models to provide accurate confidence indicators (CI). However, while it is well-known in computer vision that CI quality diminishes under distribution shift,…

Variational Quantum Algorithms (VQAs) are relatively robust to noise, but errors are still a significant detriment to VQAs on near-term quantum machines. It is imperative to employ error mitigation techniques to improve VQA fidelity. While…

Computational imaging plays a pivotal role in determining hidden information from sparse measurements. A robust inverse solver is crucial to fully characterize the uncertainty induced by these measurements, as it allows for the estimation…

Deep learning-based numerical schemes for solving high-dimensional backward stochastic differential equations (BSDEs) have recently raised plenty of scientific interest. While they enable numerical methods to approximate very…

Uncertainty quantification (UQ) plays a pivotal role in reduction of uncertainties during both optimization and decision making processes. It can be applied to solve a variety of real-world applications in science and engineering. Bayesian…

In object detection with deep neural networks, the box-wise objectness score tends to be overconfident, sometimes even indicating high confidence in presence of inaccurate predictions. Hence, the reliability of the prediction and therefore…

We propose an approximate Bayesian method for quantifying the total uncertainty in inverse PDE solutions obtained with machine learning surrogate models, including operator learning models. The proposed method accounts for uncertainty in…

We survey some of our recent results on inverse problems for evolution equations. The goal is to provide a unified approach to solve various types of evolution equations. The inverse problems we consider consist in determining unknown…

Neural networks (NNs) are currently changing the computational paradigm on how to combine data with mathematical laws in physics and engineering in a profound way, tackling challenging inverse and ill-posed problems not solvable with…

Continuous-depth neural networks, such as Neural ODEs, have refashioned the understanding of residual neural networks in terms of non-linear vector-valued optimal control problems. The common solution is to use the adjoint sensitivity…