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Reduced-order simulation is an emerging method for accelerating physical simulations with high DOFs, and recently developed neural-network-based methods with nonlinear subspaces have been proven effective in diverse applications as more…

For centuries, scientists have observed nature to understand the laws that govern the physical world. The traditional process of turning observations into physical understanding is slow. Imperfect models are constructed and tested to…

In medical imaging, scans often reveal objects with varied contrasts but consistent internal intensities or textures. This characteristic enables the use of low-frequency approximations for tasks such as segmentation and deformation field…

We present a new skeletal representation along with a matching framework to address the deformable shape recognition problem. The disconnectedness arises as a result of excessive regularization that we use to describe a shape at an…

Physics-Informed Neural Networks (PINNs) are a new family of numerical methods, based on deep learning, for modeling boundary value problems. They offer an advantage over traditional numerical methods for high-dimensional, parametric, and…

Given everyday artifacts, such as tables and chairs, humans recognize high-level regularities within them, such as the symmetries of a table, the repetition of its legs, while possessing low-level priors of their geometries, e.g., surfaces…

This work proposes a model-reduction approach for the material point method on nonlinear manifolds. Our technique approximates the $\textit{kinematics}$ by approximating the deformation map using an implicit neural representation that…

Neural fields have revolutionized the area of 3D reconstruction and novel view synthesis of rigid scenes. A key challenge in making such methods applicable to articulated objects, such as the human body, is to model the deformation of 3D…

This paper presents MetricGrids, a novel grid-based neural representation that combines elementary metric grids in various metric spaces to approximate complex nonlinear signals. While grid-based representations are widely adopted for their…

This work presents a novel physics-informed deep learning based super-resolution framework to reconstruct high-resolution deformation fields from low-resolution counterparts, obtained from coarse mesh simulations or experiments. We leverage…

Modelling complex deformation for soft robotics provides a guideline to understand their behaviour, leading to safe interaction with the environment. However, building a surrogate model with high accuracy and fast inference speed can be…

Deep Neural Networks (DNNs) have become very popular for prediction in many areas. Their strength is in representation with a high number of parameters that are commonly learned via gradient descent or similar optimization methods. However,…

Implicit Neural Representations (INRs) encoding continuous multi-media data via multi-layer perceptrons has shown undebatable promise in various computer vision tasks. Despite many successful applications, editing and processing an INR…

Neural volumetric representations have become a widely adopted model for radiance fields in 3D scenes. These representations are fully implicit or hybrid function approximators of the instantaneous volumetric radiance in a scene, which are…

Neural implicit shape representations are an emerging paradigm that offers many potential benefits over conventional discrete representations, including memory efficiency at a high spatial resolution. Generalizing across shapes with such…

Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing…

Neural fields have emerged as a powerful framework for representing continuous multidimensional signals such as images and videos, 3D and 4D objects and scenes, and radiance fields. While efficient, achieving high-quality representation…

Neural Radiance Field (NeRF) has emerged as a compelling method to represent 3D objects and scenes for photo-realistic rendering. However, its implicit representation causes difficulty in manipulating the models like the explicit mesh…

Recurrent neural networks are effective models to process sequences. However, they are unable to learn long-term dependencies because of their inherent sequential nature. As a solution, Vaswani et al. introduced the Transformer, a model…

Physics-informed neural networks (PINNs) have gained significant prominence as a powerful tool in the field of scientific computing and simulations. Their ability to seamlessly integrate physical principles into deep learning architectures…