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High-fidelity computational models of cardiac mechanics provide mechanistic insight into the heart function but are computationally prohibitive for routine clinical use. Surrogate models can accelerate simulations, but generalization across…

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…

Neural operators are neural network-based surrogate models for approximating solution operators of parametric partial differential equations, enabling efficient many-query computations in science and engineering. Many applications,…

Cardiac arrhythmogenesis is governed by complex electromechanical interactions that are not directly observable in vivo, motivating the development of non-invasive computational approaches for reconstructing three-dimensional activation…

This paper proposes a novel paradigm for machine learning that moves beyond traditional parameter optimization. Unlike conventional approaches that search for optimal parameters within a fixed geometric space, our core idea is to treat the…

Deep neural networks have shown great potential in image reconstruction problems in Euclidean space. However, many reconstruction problems involve imaging physics that are dependent on the underlying non-Euclidean geometry. In this paper,…

Modeling cardiovascular anatomies poses a significant challenge due to their complex, irregular structures and inherent pathological conditions. Numerical simulations, while accurate, are often computationally expensive, limiting their…

The correlation matrix is a central representation of functional brain networks in neuroimaging. Traditional analyses often treat pairwise interactions independently in a Euclidean setting, overlooking the intrinsic geometry of correlation…

Non-invasive electrophysiology lacks methods that accurately reconstruct whole-brain spatiotemporal dynamics while incorporating individual cortical geometry, leaving current electroencephalography and magnetoencephalography source imaging…

We propose a nonlinear manifold learning technique based on deep convolutional autoencoders that is appropriate for model order reduction of physical systems in complex geometries. Convolutional neural networks have proven to be highly…

Solving Partial Differential Equation (PDE) interface problems on varying domains is a critical task in design and optimization, yet it remains computationally prohibitive for traditional solvers. Although operator learning has shown…

Existing EEG foundation models mainly treat neural signals as generic time series in Euclidean space, ignoring the intrinsic geometric structure of neural dynamics that constrains brain activity to low-dimensional manifolds. This…

Solving partial differential equations (PDEs) efficiently and accurately remains a cornerstone challenge in science and engineering, especially for problems involving complex geometries and limited labeled data. We introduce a Physics- and…

Machine learning problems have an intrinsic geometric structure as central objects including a neural network's weight space and the loss function associated with a particular task can be viewed as encoding the intrinsic geometry of a given…

We propose a novel approach to generate samples from the conditional distribution of patient-specific cardiovascular models given a clinically aquired image volume. A convolutional neural network architecture with dropout layers is first…

Learning solution operators of partial differential equations (PDEs) from data has emerged as a promising route to fast surrogate models in multi-query scientific workflows. However, for geometric PDEs whose inputs and outputs transform…

In Artificial Intelligence (AI) and computational science, learning the mappings between functions (called operators) defined on complex computational domains is a common theoretical challenge. Recently, Neural Operator emerged as a…

This paper introduces the Neural Differential Manifold (NDM), a novel neural network architecture that explicitly incorporates geometric structure into its fundamental design. Departing from conventional Euclidean parameter spaces, the NDM…

Automated construction of surface geometries of cardiac structures from volumetric medical images is important for a number of clinical applications. While deep-learning-based approaches have demonstrated promising reconstruction precision,…

Current foundation models for electroencephalography (EEG) rely on architectures adapted from computer vision or natural language processing, typically treating neural signals as pixel grids or token sequences. This approach overlooks that…