Related papers: Encoder-decoder neural network for solving the non…

This paper proposes a new method based on neural networks for computing the high-dimensional committor functions that satisfy Fokker-Planck equations. Instead of working with partial differential equations, the new method works with an…

The increasing penetration of distributed energy resources (DERs) will decrease the rotational inertia of the power system and further degrade the system frequency stability. To address the above issues, this paper leverages the advanced…

In this work, we study linear error-correcting codes against adversarial insertion-deletion (indel) errors. While most constructions for the indel model are nonlinear, linear codes offer compact representations, efficient encoding, and…

Deep neural networks have shown great success in many diverse fields. The training of these networks can take significant amounts of time, compute and energy. As datasets get larger and models become more complex, the exploration of model…

The Boltzmann equation, a fundamental model in kinetic theory, describes the evolution of particle distribution functions through a nonlinear, high-dimensional collision operator. However, its numerical solution remains computationally…

Solving Singularly Perturbed Differential Equations (SPDEs) poses computational challenges arising from the rapid transitions in their solutions within thin regions. The effectiveness of deep learning in addressing differential equations…

Physics-Informed Neural Networks (PINNs) have emerged as a promising paradigm for solving partial differential equations (PDEs) by embedding physical laws into neural network training objectives. However, their deployment on…

Learning underlying dynamics from data is important and challenging in many real-world scenarios. Incorporating differential equations (DEs) to design continuous networks has drawn much attention recently, however, most prior works make…

This paper proposes a novel procedure for training an encoder-decoder based deep neural network which compresses NxM models into a single model enabling us to dynamically choose the number of encoder and decoder layers for decoding.…

Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…

Grokking in transformers trained on algorithmic tasks is characterized by a long delay between training-set fit and abrupt generalization, but the source of that delay remains poorly understood. In encoder-decoder arithmetic models, we…

Partial differential equations (PDEs) are widely used across the physical and computational sciences. Decades of research and engineering went into designing fast iterative solution methods. Existing solvers are general purpose, but may be…

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…

Neural network-based decoding methods show promise in enhancing error correction performance but face challenges with punctured codes. In particular, existing methods struggle to adapt to variable code rates or meet protocol compatibility…

Quantum error correction is a critical component for scaling up quantum computing. Given a quantum code, an optimal decoder maps the measured code violations to the most likely error that occurred, but its cost scales exponentially with the…

Pre-trained encoders are widely employed in dense prediction tasks for their capability to effectively extract visual features from images. The decoder subsequently processes these features to generate pixel-level predictions. However, due…

We propose the Factorized Fourier Neural Operator (F-FNO), a learning-based approach for simulating partial differential equations (PDEs). Starting from a recently proposed Fourier representation of flow fields, the F-FNO bridges the…

Surrogate strategies are used widely for uncertainty quantification of groundwater models in order to improve computational efficiency. However, their application to dynamic multiphase flow problems is hindered by the curse of…

Neural networks have shown promising potential in accelerating the numerical simulation of systems governed by partial differential equations (PDEs). Different from many existing neural network surrogates operating on high-dimensional…

Encoder-decoder-based recurrent neural network (RNN) has made significant progress in sequence-to-sequence learning tasks such as machine translation and conversational models. Recent works have shown the advantage of this type of network…