Principal Software Engineer – Circuit Simulation R&D

Graduate Researcher-Practitioner In Applied Mathematics/Statistics

At Cadence, we hire and develop leaders and innovators who want to make an impact on the world of technology. We seek a graduate researcher-practitioner in applied mathematics/statistics to advance algorithms for electronic circuit simulation, Monte Carlo yield analysis, and optimization. You will work cross-functionally to turn deep math into production-grade technology.

Qualifications:

• Graduate degree in applied mathematics, statistics, or a closely related field (CS with strong math focus).
• Demonstrated ability to conduct literature reviews, translate theory to practice, and deliver innovative results in real-world settings.

Core Expertise:

• Statistical inference: significance testing (p-values, confidence intervals), Bayesian statistics, design of experiments, Monte Carlo methods (random sampling, density estimation).
• Rare-event and reliability analysis (a plus): importance sampling, subset simulation, cross-entropy methods, extreme value/tail modeling, yield estimation.
• Surrogate modeling and Uncertainty Quantification (a plus): Gaussian processes, polynomial chaos, sparse grids, variance reduction.
• Applied Mathematics (any of the following is a plus):
• Optimization: linear, nonlinear, convex, integer, stochastic, variational; robust/multi-objective; derivative-free/global methods (e.g., CMA-ES, Bayesian optimization).
• Numerical analysis: numerical linear algebra (sparse/Krylov/preconditioning), stiff ODE/DAE solvers, approximation, quadrature; model reduction (POD/MOR).
• Differential equations: ODE/PDE/SDE, dynamical systems.
• Probability and statistics: stochastic processes, inference, uncertainty quantification.
• Data science: statistical learning, optimization for ML, dimensionality reduction.
• Familiarity with Machine Learning (preferred):
• Classical ML: regression (linear/logistic), regularization (ridge/lasso), classification (SVM, kNN), ensembles (trees, random forests, boosting).
• Contemporary AI (a plus): graph neural networks, transformers, reinforcement/transfer learning, representation learning, active learning.
• Software and Systems (Not needed but any of the following is a plus):
• Programming proficiency in Python and/or C++ is a plus (NumPy/SciPy, PyTorch/JAX, performance optimization, clean APIs).
• Strong computer science background is a plus (data structures, algorithms, version control, testing, CI/CD).
• HPC/parallel computing (a plus): MPI, CUDA, distributed workflows.
• Any prior experience in the following areas is a plus:
• Scientific computing in one or more areas: computational electromagnetics, fluid/thermal/molecular dynamics, computational physics, or electrical circuit simulation.
• Electronic design automation (EDA): SPICE/Spectre/Verilog-A, netlists, PVT/Monte Carlo flows, yield/parametric corners.

Responsibilities:

• Research, design, and validate algorithms for circuit simulation, rare-event estimation, and optimization.
• Quantify accuracy/speed vs. baselines; perform rigorous statistical analyses.
• Build robust, maintainable implementations and integrate with production toolchains.
• Good Team Player as well as collaborate with cross-functional teams and document methods and results clearly.

The annual salary range for California is $136,500 to $253,500. You may also be eligible to receive incentive compensation: bonus, equity, and benefits. Sales positions generally offer a competitive On Target Earnings (OTE) incentive compensation structure. Please note that the salary range is a guideline and compensation may vary based on factors such as qualifications, skill level, competencies and work location. Our benefits programs include: paid vacation and paid holidays, 401(k) plan with employer match, employee stock purchase plan, a variety of medical, dental and vision plan options, and more.