The Computational Applied Science Laboratory develops advanced numerical methods and computational strategies for solving complex problems in science and engineering. Our research is at the interface of Applied Mathematics, Computer Science, and Engineering Sciences.
Adaptive Grid Methods | Quad-/Oc-trees data structures enabling continuous variation in computational cell sizes for efficient multiscale simulations
Parallel Computing | Scalable algorithms designed for massively parallel architectures and distributed computing environments
Machine Learning Integration | Hybrid neuro-symbolic PDE solvers combining classical numerical methods with deep learning for forward and inverse problems
Level-Set Methods | Implicit representation of complex geometries and moving boundaries with sharp interface treatment
Deep Learning Approach for Curvature Computation in the Level-Set Method
Published in Journal of Computational Physics. This work introduces neural network architectures for high-accuracy curvature computation, achieving significant speedup over traditional numerical methods while maintaining accuracy in underresolved regions and during topological changes. Critical for applications in multiphase flows, surface tension modeling, and additive manufacturing.
Error-Correcting Neural Networks for Two-Dimensional Curvature
State-of-the-art hybrid physics-ML approach for 2D curvature computation. The error-correcting framework identifies and corrects numerical errors in real-time, providing production-ready implementation for industrial applications.
Machine Learning Algorithms for Three-Dimensional Mean-Curvature
Extension of error-correcting neural networks to three spatial dimensions, enabling accurate curvature computation in complex 3D geometries with applications in materials science and biological systems.
Error-Correcting Neural Networks for Semi-Lagrangian Advection
Neural network framework for maintaining sharp interfaces during advection in the level-set method, reducing numerical diffusion while preserving computational efficiency.
Level-Set Curvature Neural Networks: A Hybrid Approach
Combines classical numerical discretization with machine learning to leverage the strengths of both methodologies: the theoretical foundation of numerical methods and the adaptive capabilities of neural networks.
C++ Library for Hamilton-Jacobi Equations
High-order numerical methods for solving Hamilton-Jacobi equations with applications in optimal control, dynamic programming, and robotics. Features GPU acceleration and handles complex geometries through implicit interface representation.
Adaptive Mesh Refinement with p4est
Parallel adaptive mesh refinement framework using the p4est library for scalable octree-based simulations. Includes dynamic load balancing and complex geometry handling for large-scale three-dimensional computations.
Additive Manufacturing | High-resolution simulations of solidification processes in metal alloys with coupled thermal and fluid flow effects
Crystal Growth | Stefan problems and binary/multialloy growth modeling with adaptive grid refinement near moving solidification fronts
Nanostructured Polymers | Microphase separation in block copolymers with applications in energy, health, and computing sectors
High-Temperature Alloys | Phase-field modeling of Co-base and Ni-base superalloys for aerospace and power generation applications
Multiphase Flows | Level-set methods for immiscible fluids with sharp interface treatment and contact line dynamics
Turbulent Flows | Direct numerical simulation of flows over superhydrophobic surfaces for drag reduction applications
Reactive Porous Media | Coupled transport and reaction in evolving porous structures with applications in CO₂ sequestration
Compressible Reacting Flows | Ghost fluid methods for tracking detonation waves and treating stiff chemical reactions
Medical Imaging | Image-guided surgery with 3D-to-2D registration algorithms for real-time surgical navigation
Image Segmentation | Multiphase level-set segmentation with novel regularization techniques for medical and scientific image analysis
Languages: C++, Python, MATLAB, CUDA
Libraries: PETSc, MPI, p4est, JAX, TensorFlow, PyTorch
Methods: Level-Set, Finite Differences, Finite Elements, Ghost Fluid Method, Machine Learning
Infrastructure: Octree/Quadtree Grids, Adaptive Mesh Refinement, GPU Computing, Parallel Algorithms
Professor Frederic Gibou
- Faculty: Mechanical Engineering, Computer Science, Mathematics
- Editor-in-Chief: Journal of Computational Physics
- Editorial Board: Journal of Scientific Computing
- Awards: Alfred P. Sloan Fellowship, Regent's Junior Faculty Fellowship, NSF Mathematical Sciences Postdoctoral Fellowship
- Faranak Rajabi (PhD)
Our research has been published in leading journals including:
- Journal of Computational Physics
- Journal of Scientific Computing
- SIAM Journal on Scientific Computing
- Computer Physics Communications
- Physical Review E
- Physics of Fluids
Research supported by:
- National Science Foundation (NSF)
- Department of Energy (DOE)
- Office of Naval Research (ONR)
- Air Force Office of Scientific Research (AFOSR)
Lab Website | Contact | Publications
University of California, Santa Barbara | Department of Mechanical Engineering | Engineering II Building, Office 2335