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The computational overhead of traditional numerical solvers for partial differential equations (PDEs) remains a critical bottleneck for large-scale parametric studies and design optimization. We introduce a Minimal-Data Parametric Neural…

Data-driven modeling of constrained multibody dynamics remains challenged by (i) the training cost of Neural ODEs, which typically require backpropagation through an ODE solver, and (ii) error accumulation in rollout predictions. We…

Designing universal artificial intelligence (AI) solver for partial differential equations (PDEs) is an open-ended problem and a significant challenge in science and engineering. Currently, data-driven solvers have achieved great success,…

The challenge of applying learned knowledge from one domain to solve problems in another related but distinct domain, known as transfer learning, is fundamental in operator learning models that solve Partial Differential Equations (PDEs).…

Neural operators have emerged as a powerful tool for solving partial differential equations (PDEs) and other complex scientific computing tasks. However, the performance of single operator block is often limited, thus often requiring…

Thanks to their universal approximation properties and new efficient training strategies, Deep Neural Networks are becoming a valuable tool for the approximation of mathematical operators. In the present work, we introduce Mesh-Informed…

Imposing known physical constraints, such as conservation laws, during neural network training introduces an inductive bias that can improve accuracy, reliability, convergence, and data efficiency for modeling physical dynamics. While such…

The spatiotemporal resolution of Partial Differential Equations (PDEs) plays important roles in the mathematical description of the world's physical phenomena. In general, scientists and engineers solve PDEs numerically by the use of…

By learning the mappings between infinite function spaces using carefully designed neural networks, the operator learning methodology has exhibited significantly more efficiency than traditional methods in solving complex problems such as…

Precise pointer analysis is a foundational component of many client analyses and optimizations. Scaling flow- and context-sensitive pointer analysis has been a long-standing challenge, suffering from combinatorial growth in both memory…

The joint prediction of continuous fields and statistical estimation of the underlying discrete parameters is a common problem for many physical systems, governed by PDEs. Hitherto, it has been separately addressed by employing operator…

Neural operator models for solving partial differential equations (PDEs) often rely on global mixing mechanisms-such as spectral convolutions or attention-which tend to oversmooth sharp local dynamics and introduce high computational cost.…

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…

Neural PDE solvers offer a powerful tool for modeling complex dynamical systems, but often struggle with error accumulation over long time horizons and maintaining stability and physical consistency. We introduce a multiscale implicit…

Tensor networks, which are originally developed for characterizing complex quantum many-body systems, have recently emerged as a powerful framework for capturing high-dimensional probability distributions with strong physical…

Rapid and reliable solvers for parametric partial differential equations (PDEs) are needed in many scientific and engineering disciplines. For example, there is a growing demand for composites and architected materials with heterogeneous…

Simulating the time evolution of Partial Differential Equations (PDEs) of large-scale systems is crucial in many scientific and engineering domains such as fluid dynamics, weather forecasting and their inverse optimization problems.…

Numerical solvers for PDEs often struggle to balance computational cost with accuracy, especially in multiscale and time-dependent systems. Neural operators offer a promising way to accelerate simulations, but their practical deployment is…

Although very successfully used in conventional machine learning, convolution based neural network architectures -- believed to be inconsistent in function space -- have been largely ignored in the context of learning solution operators of…

Recent transformer-based architectures have shown impressive results in the field of image segmentation. Thanks to their flexibility, they obtain outstanding performance in multiple segmentation tasks, such as semantic and panoptic, under a…