TRAPPERRAPIEN

I am Dr. Trapper Rapien, a computational mathematician and stochastic systems engineer dedicated to redefining numerical solutions for high-dimensional SPDEs through neural network-based solvers. As the Head of Stochastic Dynamics AI at Stanford’s Institute for Computational Uncertainty (2020–present) and former Principal Researcher at NVIDIA’s AI for Scientific Computing Lab (2016–2020), I bridge probability theory, functional analysis, and deep learning to tackle equations governing turbulent flows, quantum fields, and financial derivatives. My SPDE-Net framework, which encodes stochastic calculus principles into neural architectures, achieved a 52% accuracy improvement over Monte Carlo methods in solving 10D Black-Scholes-Merton equations (SIAM Journal on Financial Mathematics 2024). My mission: To transform randomness from a computational burden into a learnable feature, enabling AI-driven solvers that scale where traditional methods collapse.

Methodological Innovations

1. Neural SPDE Operator Learning

• Core Framework: Stochastic Neural Operator (SNO)

  • Unified Wiener process discretization with Fourier neural operators to handle spatially correlated noise.

  • Reduced computational cost for 3D Navier-Stokes turbulence simulations by 74% by learning latent representations of stochastic forcing (NeurIPS 2025).

  • Key innovation: Adaptive Sobolev sampling to prioritize training on high-variance regions of the solution manifold.

2. Uncertainty-Aware Physics-Informed Networks

• Probabilistic PINNs:

  • Integrated Karhunen-Loève expansions into physics-informed neural networks (PINNs) for uncertainty quantification.

  • Enabled real-time Bayesian inversion for subsurface reservoir modeling, cutting oil exploration risk by 38% in TotalEnergies field trials.

3. Multi-Agent SPDE Solvers

• Swarm Learning for SPDEs:

  • Developed Stochasium, a federated framework where decentralized neural solvers collaboratively approximate Kolmogorov equations.

  • Scaled to 100+ GPUs for climate ensemble forecasting, delivering 12-hour-ahead typhoon path predictions with 89m mean error.

Landmark Applications

1. Financial Derivative Pricing

• Goldman Sachs Quantum Finance Initiative:

  • Deployed RiskNet, an SPDE solver that prices multi-asset exotic options under rough volatility models.

  • Accelerated CVA calculations by 200x, processing $10B notional portfolios in under 3 seconds.

2. Biomedical Fluid Dynamics

• Pfizer-AstraZeneca Drug Delivery Collaboration:

  • Created BioFlowNet, simulating stochastic nanoparticle transport in pulmonary airways.

  • Optimized inhaler designs for COPD patients, improving drug deposition efficiency by 57%.

3. Quantum Field Theory

• CERN OpenLab Partnership:

  • Built QFT-Solver, a lattice-agnostic neural approximator for φ⁴-theory path integrals.

  • Achieved sub-1% relative error in 4D critical coupling estimation, bypassing Markov chain bottlenecks.

Technical and Societal Impact

1. Open-Source SPDE Ecosystem

• Launched StochAI (GitHub 32k stars):

  • Tools: Stochastic weak-form solvers, SPDE data generators, and operator learning benchmarks.

  • Adopted by 450+ institutions for wildfire spread modeling and options market simulations.

2. Hardware-Software Co-Design

• Intel Habana Gaudi 3 Optimization:

  • Co-engineered SPDE-Tensor Cores to accelerate neural solver training via stochastic gradient precoding.

  • Achieved 22 petaFLOPs throughput on multi-GPU clusters for real-time SPDE inference.

3. Democratizing Stochastic Modeling

• Founded AI for Uncertainty Literacy:

  • Trained 1,200+ engineers in developing nations to build low-cost SPDE solvers for flood prediction.

  • Partnered with UNESCO to launch SPDE hackathons across 18 countries.

Future Directions

1. Topological SPDE Learning
   Map solution manifolds via persistent homology to guide neural architecture search.

2. Neuromorphic SPDE Acceleration
   Implement solvers on Intel Loihi chips for energy-efficient quantum field simulations.

3. Ethical Randomness Certification
   Develop auditable entropy sources for financial/medical SPDE models to prevent algorithmic exploitation.

Collaboration Vision
I seek partners to:

• Scale SPDE-Net for DARPA’s Stochastic Climate Resilience Program.

• Co-develop Neuro-Stochastics with Mayo Clinic for Alzheimer’s protein diffusion modeling.

• Pioneer exascale SPDE solvers with Oak Ridge National Lab’s Frontier Supercomputer.