Research

I’m interested in Computational Science and Engineering (CSE) for applications in complex biological systems. My work focuses on developing high-performance numerical methods including level-set methods, scientific computing on adaptive meshes, and solvers for nonlinear ODEs and PDEs. I’m passionate about bridging scales from molecular dynamics to continuum models using modern computational techniques.

1. Multi-Scale High-Performance Computational Methods for Free Boundary Problems

Multiscale Continuum Framework for Protein Aggregation

I’m developing a computational framework to predict long-term stability of high-concentration biotherapeutic formulations. This work addresses a critical challenge in pharmaceutical development: protein aggregation can limit drug shelf-life and cause adverse immune responses, but current models cannot bridge molecular-scale physics with shelf-life timescales.

Key contributions:

Level-set representation of evolving protein aggregate boundaries on adaptive octree grids
Continuum transport equations coupled with stochastic nucleation events
Robin boundary conditions derived from Wertheim Thermodynamic Perturbation Theory to capture surface binding affinities
Parallel implementation using the CASL library with demonstrated scaling to 1000+ cores
Integration of long-range interactions (electrostatics via Poisson-Boltzmann, hydrodynamics via Stokes flow)

Impact: This framework enables pharmaceutical companies to predict stability from short-term measurements, accelerating drug development and reducing costs.

Technologies: C++, PETSc, MPI, p4est adaptive mesh refinement, level-set methods

Status: Ongoing dissertation research (2024-2026)

2. Advanced Computational Techniques for Optimal Control

Stochastic Optimal Control for Neural Oscillators

Developed computational methods for solving stochastic Hamilton-Jacobi-Bellman (HJB) equations to design energy-efficient control strategies for noisy dynamical systems, with applications to deep brain stimulation for Parkinson’s disease.

Key contributions:

First-ever numerical framework for computing globally optimal feedback control in stochastic neural oscillator systems
High-order WENO/ENO schemes with operator splitting for HJB equations
Implicit parabolic solvers achieving 50× speedup through adaptive mesh refinement
Event-driven optimal controllers for desynchronizing pathological neural rhythms

Publications:

F. Rajabi, F. Gibou, J. Moehlis, “Optimal Control for Stochastic Neural Oscillators,” Biological Cybernetics (2025)
M. Zimet, F. Rajabi, J. Moehlis, “Nearly Optimal Chaotic Desynchronization,” IEEE CDC (2025)
J. Moehlis, M. Zimet, F. Rajabi, “Magnitude-Constrained Optimal Desynchronization,” Frontiers in Network Physiology (2025)

Technologies: C++, PETSc, adaptive mesh refinement, numerical optimal control

3. Machine Learning & AI for Science

Neural Signal Processing & Data-Driven Control

Integrating physics-informed machine learning with traditional numerical methods for time-series prediction and control optimization in biological systems.

Research directions:

Neural signal processing for extracting features from noisy neurophysiological data
Data-driven control methods combining ML with optimal control theory
Neural operators for free boundary problems: Investigating neural operator architectures (DeepONet, FNO) for accelerating level-set simulations of protein aggregation
Physics-informed neural networks (PINNs) for learning closure models in multiscale simulations

Technologies: PyTorch, JAX, TensorFlow, hybrid ML-physics approaches

Status: Active exploration (2024-2025)

4. Open-Source Scientific Solver Development

CASL-HJX: Hamilton-Jacobi Equation Solver

Developed and released CASL-HJX, the first comprehensive open-source framework for solving deterministic and stochastic Hamilton-Jacobi equations with guaranteed convergence to globally optimal solutions.

Features:

High-order accurate schemes (WENO3, WENO5, ENO) on adaptive Cartesian grids
Implicit time integration for parabolic Hamilton-Jacobi equations
Ghost fluid methods for irregular boundary conditions
Parallel implementation with MPI scaling to 1000+ cores
Comprehensive documentation and example problems

Publication: F. Rajabi, J. Fingerman, A. Wang, J. Moehlis, F. Gibou, “CASL-HJX: A Comprehensive Guide to Solving Deterministic and Stochastic Hamilton-Jacobi Equations,” Computer Physics Communications (2025)

GitHub: UCSB-CASL/CASL-HJX

GPU-Accelerated 4D HJB Solver (Work in Progress)

Currently developing a GPU-accelerated solver for 4D Hamilton-Jacobi-Bellman equations using CUDA and Kokkos for performance portability. This will enable real-time optimal control for high-dimensional dynamical systems.

Technologies: CUDA, Kokkos, C++, GPU computing

Target applications: High-dimensional stochastic control, robotics, real-time decision systems

Research Philosophy

I believe in open science and making advanced computational methods accessible. All my research code is open-source with comprehensive documentation. I’m committed to:

Developing production-quality scientific software that others can build upon
Bridging theory and practice in numerical methods
Reproducible research with version-controlled code and data
Interdisciplinary collaboration across mathematics, engineering, and biology

Collaborations & Funding

Industry: Merck Research Labs (protein aggregation modeling)
Academic: Prof. Frédéric Gibou (UCSB ME), Prof. Jeff Moehlis (UCSB ME)
Fellowships: UCSB Graduate Research Fellowship, multiple departmental awards

Want to collaborate? I’m always excited to discuss research projects, open-source contributions, or consulting opportunities in computational science. Reach out!

Faranak Rajabi