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Solving inverse problems in physics is central to understanding complex systems and advancing technologies in various fields. Iterative optimization algorithms, commonly used to solve these problems, often encounter local minima, chaos, or…
In various engineering and applied science applications, repetitive numerical simulations of partial differential equations (PDEs) for varying input parameters are often required (e.g., aircraft shape optimization over many design…
Physics-informed neural networks (PINNs) [31] use automatic differentiation to solve partial differential equations (PDEs) by penalizing the PDE in the loss function at a random set of points in the domain of interest. Here, we develop a…
One of the most popular recent areas of machine learning predicates the use of neural networks augmented by information about the underlying process in the form of Partial Differential Equations (PDEs). These physics-informed neural…
Deep learning approaches for partial differential equations (PDEs) have received much attention in recent years due to their mesh-freeness and computational efficiency. However, most of the works so far have concentrated on time-dependent…
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…
Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In…
Deep Learning is having a remarkable impact on the design of Reduced Order Models (ROMs) for Partial Differential Equations (PDEs), where it is exploited as a powerful tool for tackling complex problems for which classical methods might…
(Partial) differential equations (PDEs) are fundamental tools for describing natural phenomena, making their solution crucial in science and engineering. While traditional methods, such as the finite element method, provide reliable…
We investigate recurrent neural networks with asymmetric interactions and demonstrate that the inclusion of self-couplings or sparse excitatory inter-module connections leads to the emergence of a densely connected manifold of dynamically…
The neural network-based approach to solving partial differential equations has attracted considerable attention due to its simplicity and flexibility in representing the solution of the partial differential equation. In training a neural…
Neural operators aim to learn mappings between infinite-dimensional function spaces, but their performance often degrades on complex or irregular geometries due to the lack of geometry-aware representations. We propose the Finite Element…
Generative autoencoders offer a promising approach for controllable text generation by leveraging their latent sentence representations. However, current models struggle to maintain coherent latent spaces required to perform meaningful text…
Recent years have witnessed the promise of coupling machine learning methods and physical domain-specific insights for solving scientific problems based on partial differential equations (PDEs). However, being data-intensive, these methods…
Recently, the advent of deep learning has spurred interest in the development of physics-informed neural networks (PINN) for efficiently solving partial differential equations (PDEs), particularly in a parametric setting. Among all…
We present a framework for recovering/approximating unknown time-dependent partial differential equation (PDE) using its solution data. Instead of identifying the terms in the underlying PDE, we seek to approximate the evolution operator of…
Physical systems whose dynamics are governed by partial differential equations (PDEs) find applications in numerous fields, from engineering design to weather forecasting. The process of obtaining the solution from such PDEs may be…
This work presents a two-stage adaptive framework for progressively developing deep neural network (DNN) architectures that generalize well for a given training data set. In the first stage, a layerwise training approach is adopted where a…
Adaptability is central to autonomy. Intuitively, for high-dimensional learning problems such as navigating based on vision, internal models with higher complexity allow to accurately encode the information available. However, most learning…
Variational autoencoders (VAEs), that are built upon deep neural networks have emerged as popular generative models in computer vision. Most of the work towards improving variational autoencoders has focused mainly on making the…