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Real-world scientific applications frequently encounter incomplete observational data due to sensor limitations, geographic constraints, or measurement costs. Although neural operators significantly advanced PDE solving in terms of…

Neural PDE surrogates are often deployed in data-limited or partially observed regimes where downstream decisions depend on calibrated uncertainty in addition to low prediction error. Existing approaches obtain uncertainty through ensemble…

This work proposes an extension of neural ordinary differential equations (NODEs) by introducing an additional set of ODE input parameters to NODEs. This extension allows NODEs to learn multiple dynamics specified by the input parameter…

Open-Set Object Detection (OSOD) enables recognition of novel categories beyond fixed classes but faces challenges in aligning text representations with complex visual concepts and the scarcity of image-text pairs for rare categories. This…

Neural ordinary differential equations (NODEs) -- parametrizations of differential equations using neural networks -- have shown tremendous promise in learning models of unknown continuous-time dynamical systems from data. However, every…

We present Shape-Tailored Deep Neural Networks (ST-DNN). ST-DNN extend convolutional networks (CNN), which aggregate data from fixed shape (square) neighborhoods, to compute descriptors defined on arbitrarily shaped regions. This is natural…

Physics-informed neural networks (PINNs) have recently received much attention due to their capabilities in solving both forward and inverse problems. For training a deep neural network associated with a PINN, one typically constructs a…

Neural networks are one tool for approximating non-linear differential equations used in scientific computing tasks such as surrogate modeling, real-time predictions, and optimal control. PDE foundation models utilize neural networks to…

This paper investigates the problem of optimal predictor design for distributed parameter systems using neural networks and shape optimization. Sensors with various shapes are placed on the domain of the distributed parameter system. Data…

Energy efficiency remains a critical challenge in deploying physics-informed operator learning models for computational mechanics and scientific computing, particularly in power-constrained settings such as edge and embedded devices, where…

Recently, Neural Ordinary Differential Equations has emerged as a powerful framework for modeling physical simulations without explicitly defining the ODEs governing the system, but instead learning them via machine learning. However, the…

Partial Differential Equations (PDEs) are central to science and engineering. Since solving them is computationally expensive, a lot of effort has been put into approximating their solution operator via both traditional and recently…

Object-centric understanding is fundamental to human vision and required for complex reasoning. Traditional methods define slot-based bottlenecks to learn object properties explicitly, while recent self-supervised vision models like DINO…

We develop a new computational framework to solve sequential Bayesian optimal experimental design (SBOED) problems constrained by large-scale partial differential equations with infinite-dimensional random parameters. We propose an adaptive…

Physics-informed neural networks (PINNs) provide a promising framework for solving inverse problems governed by partial differential equations (PDEs) by integrating observational data and physical constraints in a unified optimization…

With the increased prevalence of neural operators being used to provide rapid solutions to partial differential equations (PDEs), understanding the accuracy of model predictions and the associated error levels is necessary for deploying…

This paper proposes a physics-informed neural operator (PINO) framework for solving inverse scattering problems, enabling rapid and accurate reconstructions under diverse measurement conditions. In the proposed approach, the dielectric…

One of the open problems in scientific computing is the long-time integration of nonlinear stochastic partial differential equations (SPDEs). We address this problem by taking advantage of recent advances in scientific machine learning and…

Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs) by embedding physical laws into neural network training. However, traditional PINN models are typically designed…

Neural operators have become an effective framework for learning mappings between function spaces, yet most existing architectures realize operators within a single representational domain, such as physical, spectral, or latent space. In…