Related papers: Tadpole: Autoencoders as Foundation Models for 3D …
In this paper, we propose a data-driven model reduction method to solve parabolic inverse source problems efficiently. Our method consists of offline and online stages. In the off-line stage, we explore the low-dimensional structures in the…
Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…
Physics-Informed Neural Networks (PINNs) provide a powerful and general framework for solving Partial Differential Equations (PDEs) by embedding physical laws into loss functions. However, training PINNs is notoriously difficult due to the…
High-dimensional data, particularly in the form of high-order tensors, presents a major challenge in self-supervised learning. While MLP-based autoencoders (AE) are commonly employed, their dependence on flattening operations exacerbates…
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…
Inferring parameters of high-dimensional partial differential equations (PDEs) poses significant computational and inferential challenges, primarily due to the curse of dimensionality and the inherent limitations of traditional numerical…
Recently, researchers have utilized neural networks to accurately solve partial differential equations (PDEs), enabling the mesh-free method for scientific computation. Unfortunately, the network performance drops when encountering a high…
Following its success in natural language processing and computer vision, foundation models that are pre-trained on large-scale multi-task datasets have also shown great potential in robotics. However, most existing robot foundation models…
Transfer learning paradigm has driven substantial advancements in various vision tasks. However, as state-of-the-art models continue to grow, classical full fine-tuning often becomes computationally impractical, particularly in multi-task…
We present a deep learning emulator for stochastic and chaotic spatio-temporal systems, explicitly conditioned on the parameter values of the underlying partial differential equations (PDEs). Our approach involves pre-training the model on…
This paper introduces PDEformer-1, a versatile neural solver capable of simultaneously addressing various partial differential equations (PDEs). With the PDE represented as a computational graph, we facilitate the seamless integration of…
The extensive computer-aided search applied in [arXiv:2010.10519] to find the minimal charge sourced by the fluxes that stabilize all the (flux-stabilizable) moduli of a smooth K3xK3 compactification uses differential evolutionary…
Generative adversarial network (GAN) has been shown to be useful in various applications, such as image recognition, text processing and scientific computing, due its strong ability to learn complex data distributions. In this study, a…
Positional encoding plays a crucial role in transformers, significantly impacting model performance and length generalization. Prior research has introduced absolute positional encoding (APE) and relative positional encoding (RPE) to…
Partial differential equations (PDEs) are widely used across the physical and computational sciences. Decades of research and engineering went into designing fast iterative solution methods. Existing solvers are general purpose, but may be…
Partial Differential Equations (PDEs) are fundamental for modeling physical systems, yet solving them in a generic and efficient manner using machine learning-based approaches remains challenging due to limited multi-input and multi-scale…
The field of numerical simulation is of significant importance for the design and management of real-world systems, with partial differential equations (PDEs) being a commonly used mathematical modeling tool. However, solving PDEs remains…
Deep learning-based reduced order models (DL-ROMs) have been recently proposed to overcome common limitations shared by conventional reduced order models (ROMs) - built, e.g., through proper orthogonal decomposition (POD) - when applied to…
Network embedding represents nodes in a continuous vector space and preserves structure information from the Network. Existing methods usually adopt a "one-size-fits-all" approach when concerning multi-scale structure information, such as…
Physics-constrained data-driven computing is an emerging computational paradigm that allows simulation of complex materials directly based on material database and bypass the classical constitutive model construction. However, it remains…