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In this paper we propose a new model-based unsupervised learning method, called VarNet, for the solution of partial differential equations (PDEs) using deep neural networks (NNs). Particularly, we propose a novel loss function that relies…

Partial Differential Equations (PDEs) are central to modeling complex systems across physical, biological, and engineering domains, yet traditional numerical methods often struggle with high-dimensional or complex problems. Physics-Informed…

The numerical solution of partial differential equations (PDEs) is difficult, having led to a century of research so far. Recently, there have been pushes to build neural--numerical hybrid solvers, which piggy-backs the modern trend towards…

Many problems in science and engineering can be represented by a set of partial differential equations (PDEs) through mathematical modeling. Mechanism-based computation following PDEs has long been an essential paradigm for studying topics…

The semantic segmentation of parts of objects in the wild is a challenging task in which multiple instances of objects and multiple parts within those objects must be detected in the scene. This problem remains nowadays very marginally…

Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to…

The interaction of neural networks with physical equations offers a wide range of applications. We provide a method which enables a neural network to transform objects subject to given physical constraints. Therefore an U-Net architecture…

Mathematical reasoning remains an ongoing challenge for AI models, especially for geometry problems that require both linguistic and visual signals. As the vision encoders of most MLLMs are trained on natural scenes, they often struggle to…

We describe an efficient domain decomposition-based framework for nonlinear multiscale PDE problems. The framework is inspired by manifold learning techniques and exploits the tangent spaces spanned by the nearest neighbors to compress…

We introduce a new class of spatially stochastic physics and data informed deep latent models for parametric partial differential equations (PDEs) which operate through scalable variational neural processes. We achieve this by assigning…

Partial differential equations (PDEs) form the backbone of simulations of many natural phenomena, for example in climate modeling, material science, and even financial markets. The application of physics-informed neural networks to…

Graph neural networks (GNNs) are often trained on individual datasets, requiring specialized models and significant hyperparameter tuning due to the unique structures and features of each dataset. This approach limits the scalability and…

Geometric problem solving has always been a long-standing challenge in the fields of mathematical reasoning and artificial intelligence. We built a neural-symbolic system, called FGeo-HyperGNet, to automatically perform human-like geometric…

While Transformers have demonstrated remarkable potential in modeling Partial Differential Equations (PDEs), modeling large-scale unstructured meshes with complex geometries remains a significant challenge. Existing efficient architectures…

The use of neural networks to approximate partial differential equations (PDEs) has gained significant attention in recent years. However, the approximation of PDEs with localised phenomena, e.g., sharp gradients and singularities, remains…

Graph neural networks (GNNs) have been widely used in representation learning on graphs and achieved superior performance in tasks such as node classification. However, analyzing heterogeneous graph of different types of nodes and links…

Distributed Machine Learning (DML) on resource-constrained edge devices holds immense potential for real-world applications. However, achieving fast convergence in DML in these heterogeneous environments remains a significant challenge.…

In the realm of computational science and engineering, constructing models that reflect real-world phenomena requires solving partial differential equations (PDEs) with different conditions. Recent advancements in neural operators, such as…

Accurately predicting spatio-temporal network traffic is essential for dynamically managing computing resources in modern communication systems and minimizing energy consumption. Although spatio-temporal traffic prediction has received…

Constitutive evaluations often dominate the computational cost of finite element (FE) simulations whenever material models are complex. Neural constitutive models (NCMs) offer a highly expressive and flexible framework for modeling complex…