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Memory complexity and data scarcity have so far prohibited learning solution operators of partial differential equations (PDEs) at high resolutions. We address these limitations by introducing a new data efficient and highly parallelizable…

When solving the time-dependent radiative transport equation (RTE), implicit time discretization is often employed for its robustness and stability. This results in a sequence of steady-state RTEs with identical cross-sections but varying…

Operator learning is a data-driven approximation of mappings between infinite-dimensional function spaces, such as the solution operators of partial differential equations. Kernel-based operator learning can offer accurate, theoretically…

Unlike classical artificial neural networks, which require retraining for each new set of parametric inputs, the Deep Operator Network (DeepONet), a lately introduced deep learning framework, approximates linear and nonlinear solution…

In recent years, large pre-trained Transformer networks have demonstrated dramatic improvements in many natural language understanding tasks. However, the huge size of these models brings significant challenges to their fine-tuning and…

Learning partial differential equations' (PDEs) solution operators is an essential problem in machine learning. However, there are several challenges for learning operators in practical applications like the irregular mesh, multiple input…

The radiative transfer equation (RTE) has been established as a fundamental tool for the description of energy transport, absorption and scattering in many relevant societal applications, and requires numerical approximations. However,…

Computational fluid dynamics (CFD) has become an essential tool for predicting fire behavior, yet maintaining both efficiency and accuracy remains challenging. A major source of computational cost in fire simulations is the modeling of…

Modern deep learning models operating on multi-modal visual signals often rely on inductive biases that are poorly aligned with the physical processes governing signal formation, leading to brittle performance under cross-spectral and…

Multi-task learning (MTL) is an inductive transfer mechanism designed to leverage useful information from multiple tasks to improve generalization performance compared to single-task learning. It has been extensively explored in traditional…

Traditional approaches based on finite element analyses have been successfully used to predict the macro-scale behavior of heterogeneous materials (composites, multicomponent alloys, and polycrystals) widely used in industrial applications.…

Background: Traumatic brain injury modeling requires integrating volumetric neuroimaging, demographic parameters, and acquisition metadata. Finite element solvers are too computationally expensive for clinical settings. Neural operators…

Radiation is typically the most time-consuming physical process in numerical models. One solution is to use machine learning methods to simulate the radiation process to improve computational efficiency. From an operational standpoint, this…

We propose integrating optimal transport (OT) into operator learning for partial differential equations (PDEs) on complex geometries. Classical geometric learning methods typically represent domains as meshes, graphs, or point clouds. Our…

Multimodal remote sensing semantic segmentation enhances scene interpretation by exploiting complementary physical cues from heterogeneous data. Although pretrained Vision Foundation Models (VFMs) provide strong general-purpose…

In this paper, we study the finite element operator network (FEONet), an operator-learning method for parametric problems, originally introduced in J. Y. Lee, S. Ko, and Y. Hong, Finite Element Operator Network for Solving Elliptic-Type…

Analyzing the ocean acoustic environment is a tricky task. Background noise and variable channel transmission environment make it complicated to implement accurate ship-radiated noise recognition. Existing recognition systems are weak in…

Machine-learning force fields (MLFFs) have emerged as a promising solution for speeding up ab initio molecular dynamics (MD) simulations, where accurate force predictions are critical but often computationally expensive. In this work, we…

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…

This paper proposes a learning-based framework for reconstructing 3D shapes from functional operators, compactly encoded as small-sized matrices. To this end we introduce a novel neural architecture, called OperatorNet, which takes as input…