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Physics-Informed Neural Networks (PINNs) are machine learning tools that approximate the solution of general partial differential equations (PDEs) by adding them in some form as terms of the loss/cost function of a Neural Network. Most…
The rapid global aging trend has led to an increase in dementia cases, including Alzheimer's disease, underscoring the urgent need for early and accurate diagnostic methods. Traditional diagnostic techniques, such as cognitive tests,…
Understanding and predicting the progression of neurodegenerative diseases remains a major challenge in medical AI, with significant implications for early diagnosis, disease monitoring, and treatment planning. However, most available…
Personalized medicine based on medical images, including predicting future individualized clinical disease progression and treatment response, would have an enormous impact on healthcare and drug development, particularly for diseases (e.g.…
Partial Differential Equations (PDEs) model various physical phenomena, such as electromagnetic fields and fluid mechanics. Methods like Sparse Identification of Nonlinear Dynamics (SINDy) and PDE-Net 2.0 have been developed to identify and…
Vertebral fractures are a consequence of osteoporosis, with significant health implications for affected patients. Unfortunately, grading their severity using CT exams is hard and subjective, motivating automated grading methods. However,…
Alzheimer's disease (AD) alters brain electrophysiology and disrupts multichannel EEG dynamics, making accurate and clinically useful EEG-based diagnosis increasingly important for screening and disease monitoring. However, many existing…
Diffusion Probabilistic Models (DPMs) have shown a powerful capacity of generating high-quality image samples. Recently, diffusion autoencoders (Diff-AE) have been proposed to explore DPMs for representation learning via autoencoding. Their…
We introduce a novel grid-independent model for learning partial differential equations (PDEs) from noisy and partial observations on irregular spatiotemporal grids. We propose a space-time continuous latent neural PDE model with an…
Alzheimer's disease (AD) is a heterogeneous, multifactorial neurodegenerative disorder characterized by beta-amyloid, pathologic tau, and neurodegeneration. There are no effective treatments for Alzheimer's disease at a late stage, urging…
Denoising diffusion models produce high-fidelity image samples by capturing the image distribution in a progressive manner while initializing with a simple distribution and compounding the distribution complexity. Although these models have…
This work applies concepts of artificial neural networks to identify the parameters of a mathematical model based on phase fields for damage and fracture. Damage mechanics is the part of the continuum mechanics that models the effects of…
Multi-modal generative models represent an important family of deep models, whose goal is to facilitate representation learning on data with multiple views or modalities. However, current deep multi-modal models focus on the inference of…
Generative modeling of high-dimensional data is a key problem in machine learning. Successful approaches include latent variable models and autoregressive models. The complementary strengths of these approaches, to model global and local…
We introduce deep neural networks for the analysis of anatomical shapes that learn a low-dimensional shape representation from the given task, instead of relying on hand-engineered representations. Our framework is modular and consists of…
Solving parametric Partial Differential Equations (PDEs) for a broad range of parameters is a critical challenge in scientific computing. To this end, neural operators, which \textcolor{black}{predicts the PDE solution with variable PDE…
In visual object classification, humans often justify their choices by comparing objects to prototypical examples within that class. We may therefore increase the interpretability of deep learning models by imbuing them with a similar style…
This paper explores the efficacy of diffusion-based generative models as neural operators for partial differential equations (PDEs). Neural operators are neural networks that learn a mapping from the parameter space to the solution space of…
Given genetic variations and various phenotypical traits, such as Magnetic Resonance Imaging (MRI) features, we consider two important and related tasks in biomedical research: i)to select genetic and phenotypical markers for disease…
We present a new data-driven reduced-order modeling approach to efficiently solve parametrized partial differential equations (PDEs) for many-query problems. This work is inspired by the concept of implicit neural representation (INR),…