RESEARCH PROJECTS

Physics-based deep learning frameworks have shown to be effective in accurately modeling the dynamics of complex physical systems with generalization capability across problem inputs. However, time-independent problems pose the challenge of requiring long-range exchange of information across the computational domain for obtaining accurate predictions. In the context of graph neural networks (GNNs), this calls for deeper networks, which, in turn, may compromise or slow down the training process. In this work, we present two GNN architectures to overcome this challenge - the Edge Augmented GNN and the Multi-GNN. We show that both these networks perform significantly better (by a factor of 1.5 to 2) than baseline methods when applied to time-independent solid mechanics problems. Furthermore, the proposed architectures generalize well to unseen domains, boundary conditions, and materials. Here, the treatment of variable domains is facilitated by a novel coordinate transformation that enables rotation and translation invariance. By broadening the range of problems that neural operators based on graph neural networks can tackle, this paper provides the groundwork for their application to complex scientific and industrial settings.

We present FO-PINNs, physics-informed neural networks that are trained using the first-order formulation of the Partial Differential Equation  (PDE) losses. We show that FO-PINNs offer significantly higher accuracy  in solving parameterized systems compared to traditional PINNs, and  reduce time-per-iteration by removing the extra backpropagations needed  to compute the second or higher-order derivatives. Additionally, unlike  standard PINNs, FO-PINNs can be used with exact imposition of boundary  conditions using approximate distance functions, and can be trained  using Automatic Mixed Precision (AMP) to further speed up the training.  Through two Helmholtz and Navier-Stokes examples, we demonstrate the  advantages of FO-PINNs over traditional PINNs in terms of accuracy and  training speedup.

In this project, we study the performance of an importance  sampling approach for efficient training of PINNs. Using numerical  examples together with theoretical evidences, we show that in each  training iteration, sampling the collocation points according to a  distribution proportional to the loss function will improve the  convergence behavior of the PINNs training. Additionally, we show that  providing a piecewise constant approximation to the loss function for  faster importance sampling can further improve the training efficiency.  

In this project, we use neural network surrogates to enable a faster solution approach for robust TO problems via surrogate-based optimization and build a Variational Autoencoder (VAE) to transform the the high dimensional design space into a low dimensional one. Furthermore, finite element solvers will be replaced by a neural network surrogate. Also, to further facilitate the design exploration, we limit our search to a subspace, which consists of designs that are solutions to deterministic topology optimization problems under different realizations of input uncertainties. With these neural network approximations, a gradient-based optimization approach is formed to minimize the predicted objective function over the low dimensional design subspace. 

• Developed a Video Image Processing model for the detection & classification of vehicles for Indian conditions for normal as well as extreme (DSNR) scenarios (Dense traffic, Shadows, Night time and Rainy condition) 
• Achieved a reliability of more than 90% in vehicle detection under different environmental conditions and traffic scenarios (better than the commercially available models for the same) 
• A part of Government (MoUD) sponsored project of Rs. 5 crores as a part of Centre of Excellence in Urban Transportation