Related papers: PICore: Physics-Informed Unsupervised Coreset Sele…
Simulation and optimization are crucial for advancing the engineering design of complex systems and processes. Traditional optimization methods require substantial computational time and effort due to their reliance on resource-intensive…
Accurately solving partial differential equations (PDEs) is critical to understanding complex scientific and engineering phenomena, yet traditional numerical solvers are computationally expensive. Surrogate models offer a more efficient…
Unveiling the underlying governing equations of nonlinear dynamic systems remains a significant challenge. Insufficient prior knowledge hinders the determination of an accurate candidate library, while noisy observations lead to imprecise…
PDEs arise ubiquitously in science and engineering, where solutions depend on parameters (physical properties, boundary conditions, geometry). Traditional numerical methods require re-solving the PDE for each parameter, making parameter…
Partial differential equations (PDEs) govern a wide range of physical systems, and recent multimodal foundation models have shown promise for learning PDE solution operators across diverse equation families. However, existing multi-operator…
We consider the problem of training speech recognition systems without using any labeled data, under the assumption that the learner can only access to the input utterances and a phoneme language model estimated from a non-overlapping…
Neural operators have shown promise in learning solution maps of partial differential equations (PDEs), but they often struggle to generalize when test inputs lie outside the training distribution, such as novel initial conditions, unseen…
Numerical methods such as finite element have been flourishing in the past decades for modeling solid mechanics problems via solving governing partial differential equations (PDEs). A salient aspect that distinguishes these numerical…
Mixed-dimensional partial differential equations (PDEs) are characterized by coupled operators defined on domains of varying dimensions and pose significant computational challenges due to their inherent ill-conditioning. Moreover, the…
Operator learning for partial differential equations (PDEs) aims to learn solution operators on infinite-dimensional function spaces from finite-resolution data. In this setting, it is important for the learned model to be…
Human-annotated labels are often prone to noise, and the presence of such noise will degrade the performance of the resulting deep neural network (DNN) models. Much of the literature (with several recent exceptions) of learning with noisy…
In the field of full-body reconstruction, the scarcity of annotated data often impedes the efficacy of prevailing methods. To address this issue, we introduce FuRPE, a novel framework that employs part-experts and an ingenious pseudo…
Spatiotemporal partial differential equations (PDEs) underpin a wide range of scientific and engineering applications. Neural PDE solvers offer a promising alternative to classical numerical methods. However, existing approaches typically…
Physics-informed machine learning (PIML) integrates prior physical information, often in the form of differential equation constraints, into the process of fitting machine learning models to physical data. Popular PIML approaches, including…
A primary challenge of physics-informed machine learning (PIML) is its generalization beyond the training domain, especially when dealing with complex physical problems represented by partial differential equations (PDEs). This paper aims…
The success of deep learning has been due, in no small part, to the availability of large annotated datasets. Thus, a major bottleneck in current learning pipelines is the time-consuming human annotation of data. In scenarios where such…
Several forms for constructing novel physics-informed neural-networks (PINN) for the solution of partial-differential-algebraic equations based on derivative operator splitting are proposed, using the nonlinear Kirchhoff rod as a prototype…
Physics-informed neural networks (PINNs) provide a promising machine learning framework for solving partial differential equations, but their training often breaks down on challenging problems, sometimes converging to physically incorrect…
In many scientific and engineering (e.g., physical, biochemical, medical) practices, data generated through expensive experiments or large-scale simulations, are often sparse and noisy. Physics-informed neural network (PINN) incorporates…
Solving partial differential equations (PDE) is an indispensable part of many branches of science as many processes can be modelled in terms of PDEs. However, recent numerical solvers require manual discretization of the underlying equation…