Related papers: Accelerating Legacy Numerical Solvers by Non-intru…
When solving partial differential equations using classical schemes such as finite difference or finite volume methods, sufficiently fine meshes and carefully designed schemes are required to achieve high-order accuracy of numerical…
Recently proposed gradient estimators enable gradient descent over stochastic programs with discrete jumps in the response surface, which are not covered by automatic differentiation (AD) alone. Although these estimators' capability to…
Gradient-based meta-learning methods have primarily been applied to classical machine learning tasks such as image classification. Recently, PDE-solving deep learning methods, such as neural operators, are starting to make an important…
A core capability of intelligent systems is the ability to quickly learn new tasks by drawing on prior experience. Gradient (or optimization) based meta-learning has recently emerged as an effective approach for few-shot learning. In this…
Partial differential equations frequently appear in the natural sciences and related disciplines. Solving them is often challenging, particularly in high dimensions, due to the "curse of dimensionality". In this work, we explore the…
Unconstrained optimization problems become more common in scientific computing and engineering applications with the rapid development of artificial intelligence, and numerical methods for solving them more quickly and efficiently have been…
Since annotating medical images for segmentation tasks commonly incurs expensive costs, it is highly desirable to design an annotation-efficient method to alleviate the annotation burden. Recently, contrastive learning has exhibited a great…
Fully realizing the potential of multigrid solvers often requires custom algorithms for a given application model, discretizations and even regimes of interest, despite considerable effort from the applied math community to develop fully…
Complex computer codes, for instance simulating physical phenomena, are often too time expensive to be directly used to perform uncertainty, sensitivity, optimization and robustness analyses. A widely accepted method to circumvent this…
The Portable Extensible Toolkit for Scientific Computation (PETSc) library provides scalable solvers for nonlinear time-dependent differential and algebraic equations and for numerical optimization via the Toolkit for Advanced Optimization…
The explosive demand for artificial intelligence (AI) workloads has led to a significant increase in silicon area dedicated to lower-precision computations on recent high-performance computing hardware designs. However, mixed-precision…
Stacking, a potent ensemble learning method, leverages a meta-model to harness the strengths of multiple base models, thereby enhancing prediction accuracy. Traditional stacking techniques typically utilize established learning models, such…
Bilevel optimization problems are receiving increasing attention in machine learning as they provide a natural framework for hyperparameter optimization and meta-learning. A key step to tackle these problems is the efficient computation of…
Meta-learning has been proposed as a promising machine learning topic in recent years, with important applications to image classification, robotics, computer games, and control systems. In this paper, we study the problem of using…
We consider a class of nonsmooth fractional programming problems with fixed-point constraints, where the numerator is convex and the denominator is concave. To solve this problem, we propose splitting algorithms that compute subgradient…
We propose a multi-level method to increase the accuracy of machine learning algorithms for approximating observables in scientific computing, particularly those that arise in systems modeled by differential equations. The algorithm relies…
The success of gradient-based meta-learning is primarily attributed to its ability to leverage related tasks to learn task-invariant information. However, the absence of interactions between different tasks in the inner loop leads to…
Simulating physical systems is a core component of scientific computing, encompassing a wide range of physical domains and applications. Recently, there has been a surge in data-driven methods to complement traditional numerical simulations…
Designing the next generation colliders and detectors involves solving optimization problems in high-dimensional spaces where the optimal solutions may nest in regions that even a team of expert humans would not explore. Resorting to…
The exponential growth of volume, variety and velocity of data is raising the need for investigations of automated or semi-automated ways to extract useful patterns from the data. It requires deep expert knowledge and extensive…