Related papers: Learning Deep Implicit Fourier Neural Operators (I…
This paper presents a method for modeling transient fluid flow in subsurface reservoir systems based on the developed neural operator architecture (TFNO-opt). Reservoir systems are complex dynamic objects with distributed parameters…
In the study of subsurface seismic imaging, solving the acoustic wave equation is a pivotal component in existing models. The advancement of deep learning enables solving partial differential equations, including wave equations, by applying…
Active soft bodies can affect their shape through an internal actuation mechanism that induces a deformation. Similar to recent work, this paper utilizes a differentiable, quasi-static, and physics-based simulation layer to optimize for…
We introduce a new class of non-linear models for functional data based on neural networks. Deep learning has been very successful in non-linear modeling, but there has been little work done in the functional data setting. We propose two…
A novel data-driven constitutive modeling approach is proposed, which combines the physics-informed nature of modeling based on continuum thermodynamics with the benefits of machine learning. This approach is demonstrated on…
The ever-increasing parameter counts of deep learning models necessitate effective compression techniques for deployment on resource-constrained devices. This paper explores the application of information geometry, the study of…
Gradient-based meta-learning methods have primarily been applied to classical machine learning tasks such as image classification. Recently, PDE-solving deep learning methods, such as neural operators, are starting to make an important…
With the recent rise of neural operators, scientific machine learning offers new solutions to quantify uncertainties associated with high-fidelity numerical simulations. Traditional neural networks, such as Convolutional Neural Networks…
Graph Neural Networks (GNNs) are widely used deep learning models that learn meaningful representations from graph-structured data. Due to the finite nature of the underlying recurrent structure, current GNN methods may struggle to capture…
In this paper, we propose physics-informed neural operators (PINO) that combine training data and physics constraints to learn the solution operator of a given family of parametric Partial Differential Equations (PDE). PINO is the first…
We propose INFAMOUS-NeRF, an implicit morphable face model that introduces hypernetworks to NeRF to improve the representation power in the presence of many training subjects. At the same time, INFAMOUS-NeRF resolves the classic…
We propose and study a neural operator framework for learning memory- and material microstructure-dependent constitutive laws for heterogeneous materials. We work in the two-scale setting where homogenization theory provides a systematic…
Multiscale problems are widely observed across diverse domains in physics and engineering. Translating these problems into numerical simulations and solving them using numerical schemes, e.g. the finite element method, is costly due to the…
Radiative heat transfer is a fundamental process in high energy density physics and inertial fusion. Accurately predicting the behavior of Marshak waves across a wide range of material properties and drive conditions is crucial for design…
Deep neural networks, despite their success in numerous applications, often function without established theoretical foundations. In this paper, we bridge this gap by drawing parallels between deep learning and classical numerical analysis.…
Deep-predictive-coding networks (DPCNs) are hierarchical, generative models. They rely on feed-forward and feed-back connections to modulate latent feature representations of stimuli in a dynamic and context-sensitive manner. A crucial…
We present the application of a class of deep learning, known as Physics Informed Neural Networks (PINN), to learning and discovery in solid mechanics. We explain how to incorporate the momentum balance and constitutive relations into PINN,…
Photoacoustic tomography (PAT) is a promising imaging technique that can visualize the distribution of chromophores within biological tissue. However, the accuracy of PAT imaging is compromised by light fluence (LF), which hinders the…
This work presents a physics-informed neural network approach bridging deep-learning force field and electronic structure simulations, illustrated through twisted two-dimensional large-scale material systems. The deep potential molecular…
Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…