Related papers: A scalable and accurate framework for self-calibra…

Neural networks have shown significant potential in solving partial differential equations (PDEs). While deep networks are capable of approximating complex functions, direct one-shot training often faces limitations in both accuracy and…

Image reconstruction is an inverse problem that solves for a computational image based on sampled sensor measurement. Sparsely sampled image reconstruction poses addition challenges due to limited measurements. In this work, we propose an…

Due to their uncertainty quantification, Bayesian solutions to inverse problems are the framework of choice in applications that are risk averse. These benefits come at the cost of computations that are in general, intractable. New advances…

We propose self-adaptive training---a new training algorithm that dynamically corrects problematic training labels by model predictions without incurring extra computational cost---to improve generalization of deep learning for potentially…

In this work, we propose a novel framework to enhance the efficiency and accuracy of neural operators through self-composition, offering both theoretical guarantees and practical benefits. Inspired by iterative methods in solving numerical…

Deep neural networks (DNNs) have achieved significant success across various tasks, but ensuring reliable uncertainty estimates, known as model calibration, is crucial for their safe and effective deployment. Modern DNNs often suffer from…

Ongoing developments in neural network models are continually advancing the state of the art in terms of system accuracy. However, the predicted labels should not be regarded as the only core output; also important is a well-calibrated…

Deep neural networks have become a foundational tool for addressing imaging inverse problems. They are typically trained for a specific task, with a supervised loss to learn a mapping from the observations to the image to recover. However,…

Uncertainty quantification in PDE inverse problems is essential in many applications. Scientific machine learning and AI enable data-driven learning of model components while preserving physical structure, and provide the scalability and…

Kernel methods provide a theoretically grounded framework for non-linear and non-parametric learning, with strong analytic foundations and statistical guarantees. Yet, their scalability has long been limited by prohibitive time and memory…

Accurate depth estimation is crucial for 3D scene comprehension in robotics and autonomous vehicles. Fisheye cameras, known for their wide field of view, have inherent geometric benefits. However, their use in depth estimation is restricted…

Precise sensor calibration is critical for autonomous vehicles as a prerequisite for perception algorithms to function properly. Rotation error of one degree can translate to position error of meters in target object detection at large…

Simulation-based inference (SBI) is an established approach for performing Bayesian inference on scientific simulators. SBI so far works best on low-dimensional parametric models. However, it is difficult to infer function-valued…

Reliable deep learning models require not only accurate predictions but also well-calibrated confidence estimates to ensure dependable uncertainty estimation. This is crucial in safety-critical applications like autonomous driving, which…

Inverse problems and, in particular, inferring unknown or latent parameters from data are ubiquitous in engineering simulations. A predominant viewpoint in identifying unknown parameters is Bayesian inference where both prior information…

Subspace identification methods (SIMs) have proven to be very useful and numerically robust for building state-space models. While most SIMs are consistent, few if any can achieve the efficiency of the maximum likelihood estimate (MLE).…

Solving partial differential equations is difficult. Recently proposed neural resolution-invariant models, despite their effectiveness and efficiency, usually require equispaced spatial points of data. However, sampling in spatial domain is…

We study empirical Bayes estimation in high-dimensional linear regression. To facilitate computationally efficient estimation of the underlying prior, we adopt a variational empirical Bayes approach, introduced originally in Carbonetto and…

Self-play fine-tuning has demonstrated promising abilities in adapting large language models (LLMs) to downstream tasks with limited real-world data. The basic principle is to iteratively refine the model with real samples and synthetic…

We propose new machine learning schemes for solving high dimensional nonlinear partial differential equations (PDEs). Relying on the classical backward stochastic differential equation (BSDE) representation of PDEs, our algorithms estimate…