Mathematical Scientist: Stochastic Models and Risk Quantification

Field AI is transforming how robots interact with the real world. We are building risk-aware, reliable, and field-ready AI systems that address the most complex challenges in robotics, unlocking the full potential of embodied intelligence. We go beyond typical data-driven approaches or pure transformer-based architectures, and are charting a new course, with already globally deployed solutions delivering real-world results and rapidly improving models through real-field applications.

At Field AI, we are not just building AI for robotics—we are redefining how AI systems reason under uncertainty, navigate risk, and make real-world decisions with mathematical rigor. Unlike conventional deep learning approaches that rely purely on data accumulation, our Field Foundation Models™ (FFMs) integrate stochastic analysis, differential equations, and uncertainty quantification to produce explainable, risk-aware AI capable of real-world deployment in Dull, Dirty, and Dangerous (DDD) environments.

We are seeking a mathematician specializing in stochastic differential equations (SDEs), uncertainty quantification, and risk-aware decision-making to drive first-principles AI innovation in robotics. This role is foundational to our mission, developing new mathematical paradigms that govern autonomy in the real world, ensuring explainability, robustness, and safety at every level of deployment.

• Develop stochastic models for real-time risk quantification and uncertainty propagation in robotics foundation models.
• Apply Fokker-Planck (Kolmogorov forward) equations
  , Hamilton-Jacobi-Bellman PDEs
  , and stochastic optimal control to develop explainable and physics-grounded foundation models
  .
• Develop novel stochastic inference frameworks, leveraging score-based generative models, neural stochastic differential equations (SDEs) to enable uncertainty-aware perception, state estimation, and trajectory forecasting in robotic systems
• Work on large deviations theory
  , stochastic stability
  , and rare-event simulation to model robot behavior under extreme environmental uncertainty.
• Build probabilistic programming and variational inference frameworks that enable robots to adapt dynamically to unseen conditions.
• Collaborate with our AI and engineering teams to transition mathematical insights into real-time robotics intelligence and operational decision-making
  .
• Publish novel research in stochastic control, risk-sensitive reinforcement learning, and uncertainty-aware AI,
  shaping the next era of explainable autonomy
  .

• Ph.D. in Mathematics, Applied Mathematics, Theoretical Physics
  , or a related field with a focus on stochastic processes, PDEs, or dynamical systems.
• Deep expertise in stochastic calculus
  , measure-theoretic probability
  , and functional analysis
  , with applications to uncertainty quantification and risk-aware control
  .
• Experience in Hamilton-Jacobi PDEs, path-integral control, and entropy-regularized control.
• Proficiency in high-performance computing & optimization for solving high-dimensional SDEs and PDEs at large scales (e.g., via spectral methods
  , GPU-based parallelized Monte Carlo,
  Galerkin method
  , etc.).
• Strong programming skills in Python, C++, or Julia
  , with experience in numerical computing libraries such as PyTorch, JAX, or Tensor Flow
  .
• Knowledge of Bayesian inference
  , information-theoretic approaches to decision-making
  , and probabilistic programming
  .

• Experience integrating mathematical models into real-world robotics applications is a strong plus
  .

Our salary range is between ($70,000 - $300,000 annual), but we take into consideration an individual's background and experience in determining final salary; base pay offered may vary considerably depending on geographic location, job-related knowledge, skills, and experience. Also, while we enjoy being together on-site, we are open to exploring a hybrid or remote option.

We are solving one of the world’s most complex challenges: deploying robots in unstructured, previously unknown environments. Our Field Foundational Models™ set a new standard in perception, planning, localization,…