Contributed Software

Reinforcement Learning based PDE Solvers

Deep Operator Learning

Deep Learning based PDE Solvers

Deep Learning based Governing Equation Recovery

Deep Learning for Inverse Problem and Image Processing

SelectNet

• Motivated by curriculum and self-paced learning

• Adopt a semi-supervised learning paradigm by training a deep neural network, referred to as SelectNet, to selectively add unlabelled data together with their predicted labels to the training dataset

• Provides an end-to-end approach for learning from important unlabelled data "in the wild" that most likely belong to the under-sampled classes in the training data

• The latest version of SelectNet is available here [code]

DIA-Net

• Reduce overfitting and improve generalization in deep learning

• Recurrently fuses the information from preceding layers to enhance the attention modeling at each layer

• A DIA unit via LSTM is introduced for enhancing attention

• The latest version of DIA-Net is available at https://github.com/HaizhaoYang/DIANet.

CASS

• Cross adversarial source separation (CASS) framework

• Separates an input signal consisting of a mixture of multiple components into individual components defined via adversarial learning and autoencoder fitting

• The latest version of CASS is available at https://github.com/HaizhaoYang/cass.

IEBN

• Instance Enhancement Batch Normalization: an Adaptive Regulator of Batch Noise

• An attention-based version of BN which recalibrates channel information of BN by a simple linear transformation.

• The latest version of IEBN is available at https://github.com/HaizhaoYang/IEBN.

Drop-Activation

• Reduce overfitting and improve generalization in deep learning

• Drop nonlinear activation functions by setting them to be identity functions randomly during training

• Apply a deterministic network with a new activation function to encode the average effect of dropping activations randomly

• The latest version of Drop-Activation is available at https://github.com/HaizhaoYang/Drop-Activation.

ButterflyLab

• Optimal complexity for evaluating multidimensional Fourier integral operators, special function transforms, and Green’s functions in 1D to 3D integral equations for high-frequency wave propagation.

• Optimal complexity preconditioners for high-frequency wave equations.

• The latest version of ButterflyLab for solving large-scale dense linear systems is organized and coded by Haizhao Yang and is available at https://github.com/ButterflyLab/ButterflyLab.

ButterflyPACK

• A mathematical software for rapidly solving large-scale dense linear systems that exhibit off-diagonal rank-deficiency. These systems arise frequently from boundary element methods, or factorization phases in finite-differenece/finite-element methods.

• Relies on low-rank or butterfly formats under Hierarchical matrix, HODLR or other hierarhically nested frameworks to compress, factor and solve the linear system in quasi-linear time.

• The butterfly format, originally inspired by the butterfly data flow in fast Fourier Transform, is a linear algebra tool well-suited for compressing matrices arising from high-frequency wave equations or highly oscillatory integral operators.

• The distributed and parallel version is available at https://github.com/liuyangzhuan/ButterflyPACK by Yang Liu. A sequential and easy-to-read MATLAB version is referred to ButterflyLab right above.

ELSI

• ELSI provides and enhances scalable, open-source software library solutions for electronic structure calculations in materials science, condensed matter physics, chemistry, molecular biochemistry, and many other fields. ELSI focuses on methods that solve or circumvent the Kohn-Sham eigenvalue problem in density-functional theory. The ELSI infrastructure should also be useful for other challenging eigenvalue problems.

• One of the key design pillars of ELSI is portability and support for various computing environments, from laptop-type computers all the way to the most efficient massively parallel supercomputers and new architectures (GPU and manycore processors).

• Available at https://wordpress.elsi-interchange.org/.

ZoloEig

• Interior eigenvalue solver based on fast direct solver and the best high order rational function approximation to step functions.

• Can be implemented in spectrum slicing libraries for full diagonalization.

• Can also be used to compute leading eigenpairs.

• Available at https://github.com/HaizhaoYang/zoloEig.

PSP

• The PSP is an extensible distributed-memory parallel library offering a basic set of linear algebra primitives.

• It achieves scalability and load balance via its 2D block cyclic distribution.

• Rountines for sparse data types includes (sparse) matrix (sparse) vector multiplication, (sparse) matrix (sparse) matrix multiplication, etc.

• Supports several sparse format, e.g. COO, CSC, and CSR.

• Similar user habits with Scalapack.

• Available at https://github.com/HaizhaoYang/PSP.

DeCom

• 1D to 3D Synchrosqueezed wave packet transforms for analyzing instantaneous/local properties of non-linear oscillatory signals in a superposition.

• 2D synchrosqueezed curvelet transforms for analyzing local properties of banded textures in a superposition.

• Application examples in atomic materials science, wave propagation in geophysics, biological and medical signals, and canvas painting art investigation.

• Available at https://github.com/HaizhaoYang/DeCom.

SynCrystal

• A MATLAB toolbox for atomic crystal analysis based on synchrosqueezed transforms and variational optimization.

• Automatic tool for classifying crystal lattices, identifying grain boundaries, isolated defects, estimating grain orientation and elastic deformation.

• Fast analysis for 2D and 3D atomic scale crystal data.

• Available https://github.com/SynCrystal/SynCrystal.