1.1 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.

What You Will Get To Do
• Develop stochastic models for real-timerisk 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 .

What Will Set You Apart
• Experience integrating mathematical models into real-world robotics applications is a strong plus .

• 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 TensorFlow .

• Knowledge of Bayesian inference , information-theoretic approaches to decision-making , and probabilistic programming .

Compensation and Benefits

Our salary range is between ($70,000 - $200,000 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.

Why Join Field AI?

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, and manipulation, ensuring our approach is explainable and safe for deployment.

You will have the opportunity to work with a world-class team that thrives on creativity, resilience, and bold thinking. With a decade-long track record of deploying solutions in the field , winning DARPA challenge segments, and bringing expertise from organizations like DeepMind, NASA JPL, Boston Dynamics, NVIDIA, Amazon, Tesla Autopilot, Cruise Self-Driving, Zoox, Toyota Research Institute, and SpaceX, we are set to achieve our ambitious goals.

Be Part of the Next Robotics Revolution

To tackle such ambitious challenges, we need a team as unique as our vision — innovators who go beyond conventional methods and are eager to tackle tough, uncharted questions. We’re seeking individuals who challenge the status quo, dive into uncharted territory, and bring interdisciplinary expertise. Our team requires not only top AI talent but also exceptional software developers, engineers, product designers, field deployment experts, and communicators.

We are headquartered in always-sunny Mission Viejo (Irvine adjacent), Southern California and have US based and global teammates.

Join us, shape the future, and be part of a fun, close-knit team on an exciting journey!

We celebrate diversity and are committed to creating an inclusive environment for all employees. Candidates and employees are always evaluated based on merit, qualifications, and performance. We will never discriminate on the basis of race, color, gender, national origin, ethnicity, veteran status, disability status, age, sexual orientation, gender identity, marital status, mental or physical disability, or any other legally protected status.

Salary Range: $70,000 - $200,000 USD