JAX-Based Scientific Computing Framework for Inverse Problems
The Challenge
Geophysical inverse problems—inferring subsurface structure from surface measurements—are notoriously difficult. They're ill-posed (multiple solutions fit the data), high-dimensional (millions of parameters), and computationally expensive. Commercial software was too rigid; academic code wasn't production-ready.
I needed to build a framework that could: 1. Leverage modern hardware through compilation and acceleration 2. Handle complex, realistic geological structures 3. Incorporate physical constraints (mass conservation, density bounds, drilling data) 4. Extend to new sensor types without re-engineering
Solution Overview
I architected a from-scratch Python framework solving large-scale constrained optimization problems. The system now powers production subsurface imaging workflows, transforming raw sensor data into actionable 3D density reconstructions.
Key Outcomes: - Orders of magnitude faster than traditional methods through JAX compilation - Flexible constraint system incorporating domain physics - Extensible architecture supporting multiple sensor modalities
Technical Approach
Why JAX for Scientific ML
Traditional scientific Python (NumPy/SciPy) excels at prototyping but hits performance walls at scale. JAX provides transformations that fundamentally change what's possible:
JIT Compilation: The @jax.jit decorator compiles functions to optimized XLA bytecode, delivering 10-100x speedups over pure NumPy. Computations that took minutes run in seconds.
Automatic Differentiation: jax.grad provides exact gradients of arbitrary Python functions—no manual derivation, no finite differences. Critical for gradient-based optimization where accurate derivatives mean faster convergence.
Vectorization: jax.vmap automatically parallelizes operations across batches, enabling efficient Monte Carlo sampling and ensemble computations.
Hardware Acceleration: JAX code runs on CPUs, GPUs, and TPUs with zero code changes.
Dimensionality Reduction via Parameterization
The key to tractable inverse problems is smart parameterization. Instead of optimizing millions of voxel values directly, I represent subsurface structure using smooth basis functions—reducing the search space by 1000x while maintaining physical plausibility.
This approach: - Naturally represents smooth geological features - Maintains full differentiability for gradient-based optimization - Allows complex structures through superposition of simple components
Constrained Optimization
Real inverse problems have strong prior information. I engineered a flexible constraint system using penalty methods:
- Density bounds: Physical limits on material properties
- Mass balance: Conservation laws for time-lapse scenarios
- Geometric constraints: Geomechanical realism
The loss function combines data fidelity with weighted constraint terms, allowing the optimizer to balance fitting observations against respecting physics.
Solver Integration
I integrated SciPy's optimization algorithms with JAX's automatic differentiation:
- L-BFGS-B: Quasi-Newton method for large-scale problems with box constraints
- SLSQP: Sequential quadratic programming for nonlinear constraints
The combination of exact gradients + advanced optimizers enables convergence in hundreds of iterations for problems with thousands of parameters.
Production Software Engineering
Configuration Management (Pydantic): - Type-safe configuration with runtime validation - Clear error messages for invalid inputs - Schema documentation from type hints
Modular Architecture: - Separation of concerns (data structures, forward models, optimization, visualization) - Abstract interfaces enabling easy extension to new sensor types - Comprehensive test coverage ensuring algorithmic correctness
Performance
JAX compilation transforms computational feasibility:
| Approach | Time per Iteration | 200 Iterations |
|---|---|---|
| Pure NumPy | ~15 minutes | ~50 hours |
| JAX + JIT | ~8 seconds | ~27 minutes |
110x speedup from JIT compilation alone. GPU acceleration approaches 1000x for large problems.
This transforms overnight batch jobs into interactive analysis—critical for commercial viability.
Skills Demonstrated
Scientific ML & JAX: - JIT compilation and XLA optimization - Automatic differentiation for custom loss functions - Vectorization and hardware acceleration - Gradient-based optimization at scale
Inverse Problems: - Ill-posed problem regularization - Dimensionality reduction via parameterization - Constraint formulation and penalty methods - Non-convex optimization strategies
Software Engineering: - Modular library architecture - Pydantic configuration management - Pytest for algorithmic correctness - API design for extensibility
Code Repository: Private (proprietary)
Technical Stack: Python 3.9+, JAX, NumPy, SciPy, Pydantic, Pytest
For questions about JAX-based scientific computing, contact me.
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