Related papers: CATO: Charted Attention for Neural PDE Operators

Chart comprehension presents significant challenges for machine learning models due to the diverse and intricate shapes of charts. Existing multimodal methods often overlook these visual features or fail to integrate them effectively for…

Neural operators have become increasingly popular in solving \textit{partial differential equations} (PDEs) due to their superior capability to capture intricate mappings between function spaces over complex domains. However, the…

Accurate long-term traffic forecasting remains a critical challenge in intelligent transportation systems, particularly when predicting high-frequency traffic phenomena such as shock waves and congestion boundaries over extended rollout…

Topological Deep Learning seeks to enhance the predictive performance of neural network models by harnessing topological structures in input data. Topological neural networks operate on spaces such as cell complexes and hypergraphs, that…

Neural operator learning accelerates PDE solution by approximating operators as mappings between continuous function spaces. Yet in many engineering settings, varying geometry induces discrete structural changes, including topological…

Although neural operators are widely used in data-driven physical simulations, their training remains computationally expensive. Recent advances address this issue via downstream learning, where a model pretrained on simpler problems is…

Deep neural networks based purely on attention have been successful across several domains, relying on minimal architectural priors from the designer. In Human Action Recognition (HAR), attention mechanisms have been primarily adopted on…

Understanding how the dynamics in biological and artificial neural networks implement the computations required for a task is a salient open question in machine learning and neuroscience. In particular, computations requiring complex memory…

Deep generative models have made tremendous advances in image and signal representation learning and generation. These models employ the full Euclidean space or a bounded subset as the latent space, whose flat geometry, however, is often…

We present approximation theories and efficient training methods for derivative-informed Fourier neural operators (DIFNOs) with applications to PDE-constrained optimization. A DIFNO is an FNO trained by minimizing its prediction error…

Unsupervised learning with functional data is an emerging paradigm of machine learning research with applications to computer vision, climate modeling and physical systems. A natural way of modeling functional data is by learning operators…

Neural operators are efficient surrogate models for solving partial differential equations (PDEs), but their key components face challenges: (1) in order to improve accuracy, attention mechanisms suffer from computational inefficiency on…

Neural operators learn mappings from function-dependent inputs to solutions, providing an effective framework for solving partial differential equations (PDEs). For time-dependent PDEs, existing methods typically perform long-horizon…

Attention-based Neural Networks (NN) have demonstrated their effectiveness in accurate memory access prediction, an essential step in data prefetching. However, the substantial computational overheads associated with these models result in…

A large class of inverse problems for PDEs are only well-defined as mappings from operators to functions. Existing operator learning frameworks map functions to functions and need to be modified to learn inverse maps from data. We propose a…

While the self-attention mechanism has been widely used in a wide variety of tasks, it has the unfortunate property of a quadratic cost with respect to the input length, which makes it difficult to deal with long inputs. In this paper, we…

In recent years, interest in vision-language tasks has grown, especially those involving chart interactions. These tasks are inherently multimodal, requiring models to process chart images, accompanying text, underlying data tables, and…

Data-driven learning of partial differential equations' solution operators has recently emerged as a promising paradigm for approximating the underlying solutions. The solution operators are usually parameterized by deep learning models…

Neural operators have emerged as powerful deep learning frameworks for approximating solution operators of parameterized partial differential equations (PDE). However, current methods predominantly rely on multilayer perceptrons (MLPs) for…

Medical image segmentation is a fundamental task in the community of medical image analysis. In this paper, a novel network architecture, referred to as Convolution, Transformer, and Operator (CTO), is proposed. CTO employs a combination of…