Related papers: Meta-Auto-Decoder: A Meta-Learning Based Reduced O…

Many important problems in science and engineering require solving the so-called parametric partial differential equations (PDEs), i.e., PDEs with different physical parameters, boundary conditions, shapes of computation domains, etc.…

Partial differential equations (PDEs) are often computationally challenging to solve, and in many settings many related PDEs must be be solved either at every timestep or for a variety of candidate boundary conditions, parameters, or…

Recently, Meta-Auto-Decoder (MAD) was proposed as a novel reduced order model (ROM) for solving parametric partial differential equations (PDEs), and the best possible performance of this method can be quantified by the decoder width. This…

We propose a neural network-based meta-learning method to efficiently solve partial differential equation (PDE) problems. The proposed method is designed to meta-learn how to solve a wide variety of PDE problems, and uses the knowledge for…

Solving partial differential equations (PDEs) with machine learning typically requires training a new neural network for every new equation. This optimization is slow. We introduce MetaColloc. It is an optimization-free and data-free…

Parametric partial differential equations (PDEs) are fundamental for modeling a wide range of physical and engineering systems influenced by uncertain or varying parameters. Traditional neural network-based solvers, such as Physics-Informed…

Physics-based models often involve large systems of parametrized partial differential equations, where design parameters control various properties. However, high-fidelity simulations of such systems on large domains or with high grid…

Within the framework of parameter dependent PDEs, we develop a constructive approach based on Deep Neural Networks for the efficient approximation of the parameter-to-solution map. The research is motivated by the limitations and drawbacks…

Modeling and controlling complex spatiotemporal dynamical systems driven by partial differential equations (PDEs) often necessitate dimensionality reduction techniques to construct lower-order models for computational efficiency. This paper…

System identification has greatly benefited from deep learning techniques, particularly for modeling complex, nonlinear dynamical systems with partially unknown physics where traditional approaches may not be feasible. However, deep…

The use of reduced-order models (ROMs) in physics-based modeling and simulation almost always involves the use of linear reduced basis (RB) methods such as the proper orthogonal decomposition (POD). For some nonlinear problems, linear RB…

Neural solvers for partial differential equations (PDEs) have great potential to generate fast and accurate physics solutions, yet their practicality is currently limited by their generalizability. PDEs evolve over broad scales and exhibit…

Deep learning-based reduced order models (DL-ROMs) have been recently proposed to overcome common limitations shared by conventional reduced order models (ROMs) - built, e.g., through proper orthogonal decomposition (POD) - when applied to…

Standard decoding approaches rely on model-based channel estimation methods to compensate for varying channel effects, which degrade in performance whenever there is a model mismatch. Recently proposed Deep learning based neural decoders…

The field of numerical simulation is of significant importance for the design and management of real-world systems, with partial differential equations (PDEs) being a commonly used mathematical modeling tool. However, solving PDEs remains…

We propose a reduced-order modeling approach for nonlinear, parameter-dependent ordinary differential equations (ODE). Dimensionality reduction is achieved using nonlinear maps represented by autoencoders. The resulting low-dimensional ODE…

In this work, we introduce implicit Finite Operator Learning (iFOL) for the continuous and parametric solution of partial differential equations (PDEs) on arbitrary geometries. We propose a physics-informed encoder-decoder network to…

We design a physics-aware auto-encoder to specifically reduce the dimensionality of solutions arising from convection-dominated nonlinear physical systems. Although existing nonlinear manifold learning methods seem to be compelling tools to…

We present a novel method for learning reduced-order models of dynamical systems using nonlinear manifolds. First, we learn the manifold by identifying nonlinear structure in the data through a general representation learning problem. The…

Physics-informed deep learning often faces optimization challenges due to the complexity of solving partial differential equations (PDEs), which involve exploring large solution spaces, require numerous iterations, and can lead to unstable…