Physics-constrained deterministic solution of time-dependent partial differential equations using deep convolutional encoder-decoders

Pattern recognition has its origins in engineering while machine learning developed from computer science. Today, artificial intelligence (AI) is a booming field with many practical applications and active research topics that deals with both pattern recognition and machine learning. We now use softwares and applications to automate routine labor, understand speech (using Natural Language Processing) or images (extracting hierarchical features and patterns for object detection and pattern recognition), make diagnoses in medicine, even intricate surgical procedures and support basic scientific research. This thesis deals with exploring the application of a specific branch of AI, or a specific tool, Deep Learning (DL) to solving real world engineering problems governed by Partial Differential equations which otherwise had been difficult to solve using existing methods till date. Here we focus on different Deep Learning based methods to deal with two such engineering problems. We also explore how a Deep Learning model can iteratively solve a non-linear Partial Differential Equation (PDE) based on a given set of initial conditions and using a Physics-governed loss function instead of traditional loss functions used to optimize Deep Learning models. Previous literature deal with utilizing a single loss function to solve such examples of PDE-governed systems. Moreover, the most recent work proposes to solve only a simple spatially varying PDE (Darcy Flow). We extend the framework to deal with both spatial and time-varying PDEs (Burgers\u27 Equation). Furthermore, we also propose an alternating minimization process for optimizing neural networks as PDE-solvers. This alternatively minimizes two separate loss functions. We note that this process works just as well as the single loss minimization and in certain cases, performs even better. From a neural network standpoint, we use a Convolutional Encoder-Decoder framework as our PDE-surrogate