GPU and Numerical Methods Engineer, Continuum Engine

Nebula; El Segundo (CA); Hybrid; USD 100,000 - 350,000; Full time

Benefits offered by this job

Equity participation

Health, dental, and vision insurance

401(k) with company matching

On-site work with limited WFH

Merit-based rewards

Job summary

Nebula in El Segundo is seeking a GPU and numerical methods engineer to build the linear algebra and GPU compute under a multiphysics solver stack. You will optimize matrix-free operators, Krylov solvers, and preconditioning, using Vulkan, CUDA or HIP to deliver fast, reproducible solves.

You should have a degree in CS or applied mathematics and hands-on GPU kernel experience with sparse linear algebra, mixed precision, and deterministic results.

Qualifications

• Experience with sparse/iterative linear algebra and solver analysis.
• Hands-on GPU compute kernel tuning in Vulkan, CUDA or HIP for numerical workloads.
• Ability to reason about solver pushback and performance on heterogeneous hardware.

Responsibilities

• Develop matrix-free operators for SPD systems across physics families.
• Implement Krylov solvers and preconditioning, incl. multigrid and deflation.
• Ensure convergence with fixed-order reductions and reproducibility across devices.
• Work with mixed precision and verify numerical stability in long runs.
• Profile, optimize memory layout, and perform roofline analysis.
• Collaborate on interactive tiers and distributed execution with remote accelerators.

Skills

Sparse linear algebra

Iterative solvers

Preconditioning & multigrid

GPU kernel performance

Numerical reproducibility

Education

Degree in CS / computational science / applied mathematics

Tools

Vulkan

CUDA

HIP

Job description

GPU and Numerical Methods Engineer, Continuum Engine

What to Expect

Your role is to build the linear algebra and GPU compute underneath a multiphysics solver stack, and make every solve fast, reproducible and interactive. Continuum Engine is our design and simulation tool: it turns design intent into geometry a production process can build.

The numerical side is matrix-free operators, Krylov methods and preconditioning, mixed precision and deterministic reductions. The compute side is Vulkan kernels, memory layout and occupancy judged against a roofline.

You will own the solver substrate and the performance floor: one substrate electromagnetics, conduction and elasticity share, the benchmarks that keep it from eroding, the fidelity tiers and warm sessions that keep the loop interactive, and the reproducibility guarantee every result rests on.

We are looking for computer scientists, computational scientists and applied mathematicians with experience and interest in sparse and iterative linear algebra, preconditioning and multigrid, GPU kernel performance, and numerical reproducibility.

Every role works with our AI systems daily. What can be deterministic, must be. You need no AI background; we prefer people without one. We hire for your knowledge and experience in the field first, so you can steer the ship; the tooling is a learning curve we expect you to take on.

We work on-site in El Segundo. This is hard work, but you will be rewarded with equity in a company we believe will become one of the world's most valuable.

What You'll Do

• Matrix-free operators for symmetric positive definite systems, reused across physics families rather than cloned
• Krylov solvers and preconditioning: conjugate gradient, diagonal scaling through multigrid and deflation, spectrum analysis
• Convergence discipline: true relative residual stopping and refusal to return an unconverged solve
• Mixed precision: single-precision compute with a double-precision cross-check, and error accumulation over long runs
• Reproducibility: deterministic fixed-order reductions, bitwise-identical results across devices, solution signatures, regression tests
• GPU compute: Vulkan compute shaders and SPIR-V pipelines, descriptor and buffer layout, occupancy, synchronization
• Performance engineering: roofline and bandwidth analysis, profiling, tiling and memory layout, benchmarks in regression
• Interactive tiers and distributed execution: preview, refine and full solves, warm sessions, remote accelerators

What You'll Bring

• A degree in computer science, computational science, applied mathematics or a related field, or equivalent experience
• Hands-on writing and tuning GPU compute kernels in Vulkan, CUDA or HIP for numerical workloads
• Fluent with sparse and iterative linear algebra, and able to explain why a solver stalled
• Comfortable in modern C++ inside a large codebase, and with the floating-point behavior underneath it
• The judgment to take a slow kernel back to its cause with a profiler and roofline
• Ready to build the substrate every physics family sits on, and write it to be extended
• Bonus: multigrid or domain decomposition, deterministic parallel reductions, mixed-precision refinement, or distributed accelerator execution

Expected Compensation

$100k to $350k base salary, plus equity

• Equity participation in a high-growth startup
• Comprehensive health, dental, and vision insurance
• 401(k) with company matching
• Bonus for living within 5 miles of our El Segundo facility
• On-site work with rare work-from-home exceptions
• Merit-based organization where contribution drives reward