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Numerical simulation of fluids plays an essential role in modeling many physical phenomena, which enables technological advancements, contributes to sustainable practices, and expands our understanding of various natural and engineered…

Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…

Neural networks (NNs) offer a path towards synthesizing and interpreting data on faster timescales than traditional physics-informed computational models. In this work we develop two neural networks relevant to equilibrium and shape control…

Learning representations for structured data with certain geometries (e.g., observed or unobserved) is a fundamental challenge, wherein message passing neural networks (MPNNs) have become a de facto class of model solutions. In this paper,…

The permeability of complex porous materials can be obtained via direct flow simulation, which provides the most accurate results, but is very computationally expensive. In particular, the simulation convergence time scales poorly as…

Surrogate models for the rapid inference of nonlinear boundary value problems in mechanics are helpful in a broad range of engineering applications. However, effective surrogate modeling of applications involving the contact of deformable…

Recently, physics informed neural networks (PINNs) have been explored extensively for solving various forward and inverse problems and facilitating querying applications in fluid mechanics applications. However, work on PINNs for unsteady…

Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving inverse problems, especially in cases where no complete information about the system is known and scatter measurements are available. This is especially…

We introduce methods for obtaining pretrained Geometric Neural Operators (GNPs) that can serve as basal foundation models for use in obtaining geometric features. These can be used within data processing pipelines for machine learning tasks…

Modeling molecular potential energy surface is of pivotal importance in science. Graph Neural Networks have shown great success in this field. However, their message passing schemes need special designs to capture geometric information and…

Accurately modeling complex dynamic spatio-temporal systems requires capturing flow-mediated interdependencies and context-sensitive interaction dynamics. Existing methods, predominantly graph-based or attention-driven, rely on…

In this work, physics-informed neural networks are applied to incompressible two-phase flow problems. We investigate the forward problem, where the governing equations are solved from initial and boundary conditions, as well as the inverse…

Behavior of neural networks is irremediably determined by the specific loss and data used during training. However it is often desirable to tune the model at inference time based on external factors such as preferences of the user or…

In recent years, the state-of-the-art in deep learning has been dominated by very large models that have been pre-trained on vast amounts of data. The paradigm is very simple: investing more computational resources (optimally) leads to…

Modeling the mechanics of fluid in complex scenes is vital to applications in design, graphics, and robotics. Learning-based methods provide fast and differentiable fluid simulators, however most prior work is unable to accurately model how…

In this study, we have explored an application of deep learning architecture of the U-Net model, originally designed for biomedical image segmentation, in a regression analysis aimed at predicting fluid flows through textured microchannels.…

While both shape and texture are fundamental to visual recognition, research on deep neural networks (DNNs) has predominantly focused on the latter, leaving their geometric understanding poorly probed. Here, we show: first, that optimized…

We propose a novel neural network architecture, SwitchNet, for solving the wave equation based inverse scattering problems via providing maps between the scatterers and the scattered field (and vice versa). The main difficulty of using a…

Microfluidics have shown great promise in multiple applications, especially in biomedical diagnostics and separations. While the flow properties of these microfluidic devices can be solved by numerical methods such as computational fluid…

To facilitate widespread adoption of automated engineering design techniques, existing methods must become more efficient and generalizable. In the field of topology optimization, this requires the coupling of modern optimization methods…