Zero Coordinate Shift: Whetted Automatic Differentiation for Physics-informed Operator Learning

1 code implementation • 1 Nov 2023 • Kuangdai Leng, Mallikarjun Shankar, Jeyan Thiyagalingam

Automatic differentiation (AD) is a critical step in physics-informed machine learning, required for computing the high-order derivatives of network output w. r. t.

Operator learning Physics-informed machine learning

Padding-free Convolution based on Preservation of Differential Characteristics of Kernels

no code implementations • 12 Sep 2023 • Kuangdai Leng, Jeyan Thiyagalingam

Convolution is a fundamental operation in image processing and machine learning.

Image Classification Semantic Segmentation +1

On the Compatibility between Neural Networks and Partial Differential Equations for Physics-informed Learning

1 code implementation • 1 Dec 2022 • Kuangdai Leng, Jeyan Thiyagalingam

Inspired by this pitfall, we prove that a linear PDE up to the $n$-th order can be strictly satisfied by an MLP with $C^n$ activation functions when the weights of its output layer lie on a certain hyperplane, as called the out-layer-hyperplane.