Related papers: Universal Solution Manifold Networks (USM-Nets): n…

Partial differential equations (PDEs) form the mathematical foundation for modeling physical systems in science and engineering, where numerical solutions demand rigorous accuracy-efficiency tradeoffs. Mesh movement techniques address this…

Accurate modeling of complex physical problems, such as fluid-structure interaction, requires multiphysics coupling across the interface, which often has intricate geometry and dynamic boundaries. Conventional numerical methods face…

Numerical solutions of partial differential equations (PDEs) require expensive simulations, limiting their application in design optimization, model-based control, and large-scale inverse problems. Surrogate modeling techniques seek to…

Nonlinear finite element crash simulations are accurate but computationally expensive, limiting their use in iterative design optimisation. Machine-learning surrogate models based on graph neural networks (GNNs) offer a faster alternative.…

Mesh-based simulations play a key role when modeling complex physical systems that, in many disciplines across science and engineering, require the solution of parametrized time-dependent nonlinear partial differential equations (PDEs). In…

State-of-the-art computer codes for simulating real physical systems are often characterized by a vast number of input parameters. Performing uncertainty quantification (UQ) tasks with Monte Carlo (MC) methods is almost always infeasible…

Machine learning-based surrogate models have emerged as more efficient alternatives to numerical solvers for physical simulations over complex geometries, such as car bodies. Many existing models incorporate the simulation mesh as an…

Medical image segmentation is a critical task in medical imaging analysis. Traditional CNN-based methods struggle with modeling long-range dependencies, while Transformer-based models, despite their success, suffer from quadratic…

We propose a non-intrusive method to build surrogate models that approximate the solution of parameterized partial differential equations (PDEs), capable of taking into account the dependence of the solution on the shape of the…

We present a new approach for nonlinear dimensionality reduction, specifically designed for computationally expensive mathematical models. We leverage autoencoders to discover a one-dimensional neural active manifold (NeurAM) capturing the…

This study explores the potential of graph neural networks (GNNs) to enhance semantic segmentation across diverse image modalities. We evaluate the effectiveness of a novel GNN-based U-Net architecture on three distinct datasets: PascalVOC,…

Algebraic or geometric multigrid methods are commonly used in numerical solvers as they are a multi-resolution method able to handle problems with multiple scales. In this work, we propose a modification to the commonly-used U-Net neural…

Many imaging problems require computing spatial transformations induced by spatially varying intensity, feature, or density fields. Canonical examples include distortion correction, deformable image registration, atlas-based segmentation,…

Solving complex Partial Differential Equations (PDEs) accurately and efficiently is an essential and challenging problem in all scientific and engineering disciplines. Mesh movement methods provide the capability to improve the accuracy of…

Ultrasound is widely used in clinical practice due to its affordability, portability, and safety. However, current AI research often overlooks combined disease prediction and tissue segmentation. We propose UniUSNet, a universal framework…

Generalization capabilities of learning-based medical image segmentation across domains are currently limited by the performance degradation caused by the domain shift, particularly for ultrasound (US) imaging. The quality of US images…

Numerical simulation of multi-phase fluid dynamics in porous media is critical to a variety of geoscience applications. Data-driven surrogate models using Convolutional Neural Networks (CNNs) have shown promise but are constrained to…

Unsupervised skin lesion segmentation offers several benefits, including conserving expert human resources, reducing discrepancies due to subjective human labeling, and adapting to novel environments. However, segmenting dermoscopic images…

Data-driven modeling approaches can produce fast surrogates to study large-scale physics problems. Among them, graph neural networks (GNNs) that operate on mesh-based data are desirable because they possess inductive biases that promote…

Traditional methods for high-dimensional diffeomorphic mapping often struggle with the curse of dimensionality. We propose a mesh-free learning framework designed for $n$-dimensional mapping problems, seamlessly combining variational…