Our research on Scientific Machine Learning (SciML) and differentiable programming focuses on discovering new physics and developing fast algorithms to accelerate numerical simulations.

## Open Source Code implementations of SciML

### Graph Network Simulator (GNS)

Graph Network-based Simulator (GNS) is a framework for developing generalizable, efficient, and accurate machine learning (ML)-based surrogate models for particulate and fluid systems using Graph Neural Networks (GNNs). GNS code is a viable surrogate for numerical methods such as Material Point Method, Smooth Particle Hydrodynamics and Computational Fluid dynamics. GNS exploits distributed data parallelism to achieve fast multi-GPU training. The GNS code can handle complex boundary conditions and multi-material interactions.

### Differentiable MPM (DiffMPM)

DiffMPM (Differentiable Material Point Method) is an innovative approach that brings differentiability to the Material Point Method (MPM). By enabling gradients to flow through MPM simulations, DiffMPM unlocks a new frontier in physics-based optimization and machine learning tasks, bridging the gap between computational mechanics and deep learning paradigms. Leveraging the core principles of MPM, which provides a robust mechanism for simulating complex materials and large-deformation problems, DiffMPM enhances this capability by allowing for end-to-end optimization of simulation parameters, thereby opening doors to novel applications in additive manufacturing, robotics, and design. Our research group delves deep into exploring the potential of DiffMPM and its implications in both theoretical advancements and practical applications.

## Simulations

## Videos

X-AI and Machine Learning, 2022 SimCenter-DesignSafe AI workshop

## Team

## Publications

### Inverse analysis of granular flows using differentiable graph neural network simulator

Choi, Y.J, Kumar, K.;

### Graph Neural Network-based surrogate model for granular flows

Choi, Y.J, Kumar, K.;

*Computers and Geotechnics*

### Three-dimensional granular flow simulation using graph neural network-based learned simulator

Choi, Y.J, Kumar, K.;

### Accelerating particulate and fluid simulations with graph neural networks for solving forward and inverse problems

Kumar, K., Choi, Y.J.;

### Differentiable programming for inverse estimation of soil permeability and design of duct banks

Vajapeyajula, A., Kumar, K.;

### An inverse analysis of fluid flow through granular media using differentiable lattice Boltzmann method

Wang, Q., Kumar, K.;

### Enabling knowledge discovery in natural hazard engineering datasets on DesignSafe

Mehta, C., Kumar, K.;

### Geotechnical Parrot Tales (GPT): Harnessing Large Language Models in geotechnical engineering

Kumar, K.;

### GNS: A generalizable Graph Neural Network-based simulator for particulate and fluid modeling

Kumar, K., Vantassel, J.;

### Using explainability to design physics-aware CNNs for solving subsurface inverse problems

Crocker, J., Kumar, K., Cox, B.;

### Evaluation of particle motions in stabilized specimens of transparent sand using deep learning segmentation

Marx, D., Kumar, K., Zornberg, J.;

### A frequency-velocity CNN for developing near-surface 2D Vs images from linear-array, active-source wavefield measurements

Abbas, A, Vantassel, J., Cox, B. R., Kumar, J., Crocker, J;

### Minority Report: A graph network oracle for in situ visualization

Kumar, K., Navratil, P., Solis, A., Vantassel, J;

### A machine learning approach to predicting pore pressure response in liquefiable sands under cyclic loading

Choi, Y., Kumar, K.;

### Using Convolutional Neural Networks (CNN) to develop starting models for 2D full waveform inversion

Vantassel, J. P.;
Kumar, K.;
Cox, B. R.;

*Geophysics*