Research Highlights

Following is a list of selected highlights from the FASTMath Institute.

2025:

• Condensed Stein Variational Gradient Descent 

• Federated Learning on Stochastic Neural Networks 

• Uncertainty Quantification of Neural Network Models via Langevin Sampling

• Embedded Nonlocal Operator Regression (ENOR): Quantifying Model Error in Learning Nonlocal Operators 

• Robust approaches to big data summarization 

• New particle adaptivity technique in PETSc/TAO 

• Surrogate Modeling of MHD Flows for Liquid Metal Fusion Blankets 

• Efficient Eigenvalue Computation for Nuclear Structure Calculations

• Inexact Subspace Projection Methods for Tensor Eigenvalue Problems

• Disentangling Latent Spaces in AI/ML Generative Models for Scientific Datasets 

• Multi-fidelity Stochastic Optimization 

• Globally Optimal Designs 

• Robust Design of Experiments 

• Construction of H2 Matrices on GPUs

• ShyLU node: On-node Scalable Solvers and Preconditioners  Recent Progress and Current Performance

• Statistical treatment of HPC latencies in iterative methods

• Training AI from In Situ ML Framework for PDEs

• Stellarator Geometry, Meshing and Code Coupling Technologies 

• GPU Acceleration of Monte Carlo Tallies on Unstructured Meshes in OpenMC

• Parallel Unstructured Mesh Infrastructure for Particle Simulations 

• MFEM Facilitates the Design of More Robust Fusion System RF Antennas

• Jet: A Multilevel Graph Partitioner for GPU

• Theoretical Training Guaranties for Stochastic Neural Networks (SNN) 

• Variable Order Multigrid Data Compression With MGARD

• Variable order compression 

• Compressing unstructured data  

• Adaptive replication cuts oracle queries in noisy optimization 

• Multi-fidelity methods for quantifying uncertainty in sea-level projections 

2024:

• Robust Optimal Experimental Design for Nonlinear Inverse Problems 

• Probabilistic Approach to Combinatorial Optimization 

• Exploiting Structure for Fast Solvers in Tokamak models

• New Operator Splitting Module in SUNDIALS

• Enabling Applications with Many Independent ODEs at Exascale with SUNDIALS

• Impact of hypre on applications

• New FASTMath software package releases for use in the xSDK ecosystem

• Heuristics for Robust Factorization of Sparse Symmetric Indefinite Matrices

• GPU Accelerated Sparse Cholesky Factorization

2023:

• Dispersion Enhanced Sequential Batch Sampling For Adaptive Contour Estimation

• ARKODE Infrastructure for Advanced Time Integration Methods

• Butterfly-Compressed Green’s Functions for High-Frequency Helmholtz Equations with Variable Coefficients

• Adaptive Mesh Refinement (AMR) Application Interfaces for Time Integrators: SUNDIALS Library Integration with Chombo AMR Impacts BISICLES Ice Sheet Model

• Maintaining Trust in Data Reduction

• Accelerated and Accurate Data Assimilation

• Efficient Eigensolvers for Nuclear Structure Calculations

• Scaling Iterative Eigenvalue Solvers on GPU-Based Supercomputers

• Advanced PDE-constrained Optimization Capability for Ice Sheet Calibration

• Structure Preserving, HPC Landau Collision Operator for Runaway Electron Mitigation

• Multiobjective Optimization Methods for the LCLS-II Photoinjector

• Adaptive and Automatic ML Reduced Order Model Creation

• Accuracy-Based Controls for Multirate Time Step Selection

• Multirate Methods for Coupled Compressible Navier-Stokes Systems

• Structure-Aware Methods for Expensive Derivative-Free Nonsmooth Composite Optimization

• Bayesian Calibration for Xenon Diffusion in UO2 Nuclear Fuel

• Batched All GPU Solvers for Many Small System Solves in PETSc

• PETSc Multigrid Solvers for Magnetohydrodynamics in FES

• PyOED: Extensible Suite for Optimal Design of Experiments

• Detecting Resonance of Accelerator Cavities Using Fast Direct Integral Equation Solvers and Augmented Bayesian Optimization

• Robust Optimal Experimental Design

• Machine Learning for Space Weather Mitigation

• A New Algebraic Multigrid Solver for Semi-Structured Linear Systems

• SUNDIALS Numerical Library Team Wins Prestigious Prize

• Recent Algorithm Development in SuperLU_DIST Sparse Direct Solver for SciDAC Applications

2022:

• Surrogate Modeling via Functional Tensor Networks in Arbitrary Formats

• Using ParMOO to Drive Materials Design

• Uncertainty Quantification for Fusion Plasma-Surface Interactions

• Dynamic AMR for a Relativistic Electron Drift-Kinetic Solver and Scalable PETSc-p4est Implementation and Implicit Time Stepping

• Parallel Unstructured Mesh Infrastructure for PIC (PUMIPic) and its integration into Tokamak Edge Plasma (XGCm) and Impurity Transport (GITRm) Codes

• MFEM Facilitates the Design of More Robust Tokamak RF Antennas: High-order Methods on Adaptive Unstructured Meshes (updated)

• A New Algebraic Multigrid Solver for Semi-structured Linear Systems

• Fast and Flexible Monolithic AMG Framework for Multiphysics PDE Systems

2021:

• Bidirectional Data Movement In Situ Accelerates Time to Insight

• Dynamic Load Balancing for Particle-in-Cell Codes: EnGPar

• Computational Tools for Exascale Fusion Simulations

• Portable Structure Preserving Kinetic Methods for Fusion Plasmas

• Scalable Implicit, Adaptive MFEM-based Solver for Reduced Resistive MHD

• MFEM Miniapps Enhance Tokamak Simulations

• Scalable Preconditioners for Tokamak Applications in MFEM

• MFEM Facilitates the Design of More Robust Tokamak RF Antennas: High-order Methods on Adaptive Unstructured Meshes

• Hierarchical Partitioning for Distributed Multi-GPU Platforms

• Parallel Unstructured Mesh Infrastructure for PIC (PUMIPic) and its Integration into Tokamak Edge Plasma (XGCm) and Impurity Transport (GITRm) Codes

• Multiscale/Multirate Modeling of ITG/ETG Tokamak Turbulence

• New Multirate Time Integrators Enable Greater Efficiency in Multiscale Problems

• Fast and Flexible Monolithic AMG Framework for Multiphysics PDE Systems

• Batched All GPU Controlled Solvers for Many Small Systems

• Low-complexity Sparse Direct Solvers for Wave Equations

• New Low Synchronization Methods Speed Up Anderson Accelerated Nonlinear Solvers

• SuperLU: Sparse Triangular Solve on multi-GPUs

• Solving Neural Ordinary Differential Equations with PETSc

• Learning Stiff Hamiltonian Systems from Data

• Anderson Accelerated Solvers for Faster Fusion Simulations

• Improving Dense Block Structure in Sparse Matrix Factorization

• New Algebraic Multigrid Solver for Semi-structured Problems

• Solving Eigenvalue Problem with Localized Eigenvectors using Reinforcement Learning

• Enhancing Scalability of a Matrix-Free Tensor Eigensolver for Studying Many-Body Localization

• Bilevel and Robust Optimization for Automated Tuning of HEP Event Generators

• Optimal Design of Electro-Magnetic Cloaks using Fast Solvers for Mixed-Integer PDE-Constrained Optimization

• Differentiable ODE Solvers for PDE-constrained Optimization and Scientific Machine Learning

• Training Neural Networks Under Physics Constraints: Approximating the Fokker-Planck-Landau Collision Operator for XGC

• TAD: Targeted Adaptive Design

• Uncertainty Quantification for Impurity Transport Model

• Batch Greedy Algorithms and Guarantees for Optimal Experimental Design

• Multifidelity Uncertainty Quantification for Tokamak Disruption Simulation (TDS)

• Haar-Like Wavelets on Clustered Point Clouds

• Parameter Estimation from Observational Data using ML Method

• Capturing Euclidean Metric Structure with Randomized Trees

• Data Analytics of Streaming Scientific Data

• Performance Optimization for Large-scale Eigenvalue Computation [FASTMath-RAPIDS collaboration]

• Source Code and Algorithm Optimizations Speed Up Nuclear Physics Simulations [FASTMath-RAPIDS collaboration]

• Bidirectional Data Movement In Situ Accelerates Design Space Optimization [FASTMath-RAPIDS collaboration]

• MGARD Data Compression Tool: v1 Release [FASTMath-RAPIDS collaboration]

• Machine Learning-Based Inversion of Nuclear Responses [FASTMath-RAPIDS collaboration]

• Optimal Design and Control with Machine-Learning Surrogates [FASTMath-RAPIDS collaboration]

• FASTMath-RAPIDS Interaction: Coupling Fusion Codes via ADIOS2 and EFFIS 2.0 [FASTMath-RAPIDS collaboration]

• CTTS-FASTMath-RAPIDS Partnership [FASTMath-RAPIDS collaboration]