Modeling and simulation are critical elements of discovery science. They help us better understand our physical world, especially phenomena that cannot be fully grasped through observation or experimentation alone. These systems might be enormous, like the structure formation of our universe, or minuscule, like quantum chemistry and microelectronics design. They could also involve extremely fast processes, such as those in particle physics, or very slow ones, like climate change and stellar evolution. By shedding light on the underlying mechanisms of a system, simulations enable researchers to predict how these systems will behave in the future.

At Berkeley Lab, we develop state-of-the-art methodologies and techniques to understand and predict both continuous (measurable) and discrete (countable) aspects of physical systems—like hurricanes or traffic flow—and their dynamic behavior. We ensure that the mathematical characteristics of our models are accurate so that researchers can rely on the results. Our models and simulations can be run on computers of all scales, from laptops to modern supercomputers.

Our mathematicians, computational scientists, and data scientists collaborate with researchers from various disciplines to model complex systems, including the intricate dynamics of commercial spray painting, wind farms, transportation networks, computer hardware, fluid flows, and much more.

 3D visualization of fluid turbulence simulation inside a transparent, funnel-shaped vessel, showing green and yellow turbulent flow structures.

AMReX is a leading open-source software framework for massively parallel simulations with adaptive mesh refinement (AMR). It supports complex multiphysics applications in astrophysics, fusion, combustion, and microelectronics, and is widely used by DOE Exascale Computing Projects.

 Cut-away view of a cubed sphere atmospheric test problem, displaying a Hadley cell-like vertical velocity field with alternating red and blue regions representing upward and downward motion within the spherical grid structure.

Chombo is a flexible, widely adopted open-source AMR framework tailored for structured grid applications and complex partial differential equations. Known for its versatility and robust support for multiphase flows, magnetohydrodynamics, and industrial processes, Chombo enables researchers to tackle challenging geometries and legacy scientific codes with ease.

 A colorful 3D visualization of complex geological formations, featuring vibrant shades of green, blue, orange, and red. The image includes intricate textures and patterns, with black arrows indicating flow directions or data points. This visualization highlights advanced computational techniques used to analyze and interpret geological structures.

Chombo-Crunch is a high-performance simulator for flow and transport in complex, heterogeneous materials, scalable on DOE supercomputers and GPU-ready. Its unique ability to run direct simulations from image data drives advances in subsurface science—such as carbon sequestration and fracture evolution—and powers engineering applications from battery electrodes to manufacturing.

 Visualization of a complex computational model featuring a lattice structure with hexagonal cells, containing red and blue clusters representing data points or molecular interactions. This image is associated with a paper by Mauro Del Ben and Charlene Yang, recognized as a finalist for the ACM Gordon Bell Prize for achievements in high performance computing.

BerkeleyGW is a state-of-the-art software package for excited-state calculations in quantum materials. It enables high-fidelity simulations of electronic structure and optical properties, supporting advances in materials for quantum information science and next-generation electronics.

 A circular grayscale image showing the reconstruction of nano-CT data with sparse projection angles using 202 projections. The image features various dark and light spots indicating different densities or compositions within the material. A small square within the circle highlights a specific area of interest for detailed analysis. This reconstruction demonstrates the effectiveness of advanced imaging techniques in suppressing noise and improving computational speed.

TomoCAM is an open-source algorithm that reconstructs 3D images from X-ray tomography data at record speed and accuracy. It’s used for rapid analysis of complex materials and supports real-time feedback at experimental facilities.

 Diagram illustrating a feedback loop between experiments, mathematical reconstruction, and self-driving experiments. On the left, an experiment produces a complex data pattern, which flows through mathematical equations and leads to a 3D molecular reconstruction on the right. Below, a surface plot represents the optimization process of self-driving experiments, completing the cycle. The CAMERA Applied Math logo is in the lower right corner.

CAMERA (Center for Advanced Mathematics for Energy Research Applications) develops new mathematics and algorithms for experimental data interpretation, uncertainty quantification, and real-time autonomous experiments at DOE user facilities, directly linking simulation and experiment.

 Screenshot of a scientific software interface showing automated calibration of silver behenate data. The center panel displays overlapping yellow and green rings, indicating alignment, and a graph at the bottom shows the resulting one-dimensional spectrum.

Xi-cam is an open-source platform for high-throughput data management, visualization, and analysis, bridging experimental data with simulation workflows in materials and photon science.

 A small green plant growing inside a transparent, rectangular plastic chamber with metal fasteners, placed on a black background.

RhizoNet leverages AI to analyze plant root images, enabling automated, high-throughput phenotyping and supporting self-driving laboratory experiments in agricultural research.

 The image displays three colorful, three-dimensional graphs with peaks and valleys, each representing different data sets or functions. The graphs are rendered in vibrant shades of blue, green, and purple, and are positioned against a dark background with faint mathematical equations or diagrams. The visual suggests a focus on data analysis or mathematical modeling.

SuperLU is a high-performance library for solving large, sparse linear systems using direct LU factorization. With support for MPI, OpenMP, and CUDA, it delivers scalable performance on modern HPC systems, making it a cornerstone for accurate and efficient scientific simulations.

 Visualization of the ITER tokamak, the largest fusion device of its kind when built. The image highlights the use of SuperLU and STRUMPACK solvers in simulation codes for projects like ITER, showcasing advanced computational methodologies.

STRUMPACK is a scalable solver for sparse and dense linear systems, specializing in matrices with hierarchical low-rank structure. Its advanced compression techniques and strong GPU and distributed memory support enable fast, memory-efficient solutions for large-scale modeling and simulation tasks.

 Colorful computer-generated simulation of a hydrogen swirl. Digitally-generated cross-section of mathematically-simulated water waves. A 3d display of a simulated High Luminosity LHC collision event as seen by the ATLAS inner tracking detector (ITk). Image: Atlas Collaboration.
Last edited: December 18, 2025