We Are Synopsys is the leader in engineering solutions from silicon to systems, enabling customers to rapidly innovate AI-powered products. We deliver industry-leading silicon design, IP, simulation and analysis solutions, and design services. We partner closely with our customers across a wide range of industries to maximize their R&D capability and productivity, powering innovation today that ignites the ingenuity of tomorrow. You Are You have spent years building software where the math actually matters, where a poorly tuned parameter or a slow convergence algorithm does not just make a demo sluggish, it blocks a customer from shipping a chip on schedule. You know that optimization is not about throwing gradient descent at a problem and hoping, it is about understanding the physics, the data, and the tradeoffs well enough to know which knobs to turn and when to stop. You are comfortable moving between complex C++ implementations and Python prototyping, between statistical outlier analysis and conversations with field engineers who need you to explain why a model is behaving the way it is. You do not wait for perfect datasets or fully specified requirements. You dig into noisy data, ask the right questions, and build models that hold up under real-world manufacturing conditions. The problems you like are the ones where the solution is not in a textbook. Where you have to combine numerical methods, domain knowledge, and engineering judgment to get something that works. Maybe you are finishing a PhD where you built custom optimization algorithms for physical systems, or you have a few years in industry applying advanced mathematical modeling to real engineering problems. Either way, you bring both theoretical depth and the practical instinct to know when theory needs to bend to reality. At Synopsys, you will work on computational lithography models that enable the next generation of semiconductor manufacturing, and the team you join will expect you to bring both rigor and creativity to problems that have never been solved before. What You'll Be Doing • Design and implement optimization techniques that reduce model calibration runtime without sacrificing accuracy, working directly with large-scale empirical datasets from leading-edge semiconductor processes • Prototype and develop new mathematical models for lithography simulation, translating specifications into production-quality C++ code integrated into the Proteus product line • Calibrate and tune complex non-linear model parameters using statistical analysis, numerical optimization, and domain-specific heuristics • Collaborate with cross-functional teams including product engineering, field support, and customer-facing teams to understand technical requirements and integrate modeling solutions into existing workflows • Analyze outlier data points and develop sampling strategies that improve model robustness and generalization across process variations • Maintain and extend existing computational lithography models, diagnosing performance bottlenecks and correctness issues in a large, mature codebase • Work directly with field engineers and customers to troubleshoot model behavior, gather requirements for new features, and validate solutions against real manufacturing data The Impact You Will Have • Enable semiconductor manufacturers to bring next-generation nodes to production faster by delivering models that calibrate in hours instead of days • Unlock previously unsolvable lithography challenges by developing optimization techniques that handle higher complexity and tighter tolerances than existing methods • Improve model accuracy across a wider range of manufacturing conditions, reducing costly silicon respins and accelerating time to market for customers • Strengthen Synopsys' competitive position in computational lithography by contributing novel algorithms and methods that differentiate the Proteus platform • Reduce customer escalations and support load by building models that are more robust, interpretable, and easier to tune in the field • Influence product roadmap and strategy by identifying technical gaps and opportunities based on direct customer interaction and data analysis • Mentor and raise the technical bar for the broader modeling team by sharing deep expertise in optimization, numerical methods, and software engineering best practices What You'll Need • PhD in Computer Science, Electrical Engineering, Physics, Applied Mathematics, or related field strongly preferred (recent PhD graduates encouraged to apply; PhD with 1-2 years of industry experience ideal), OR MS in a related field with approximately 5 years of directly relevant industry experience in computational modeling, optimization, or numerical methods • Strong programming skills in C++ for performance-critical numerical software and Python for prototyping and data analysis • Deep background in physical modeling, statistical analysis, and optimization methods, with hands-on experience applying these techniques to real-world problems • Solid foundation in numerical computation, including experience with algorithms for solving non-linear systems, parameter fitting, and convergence analysis • Demonstrated ability to analyze complex datasets, identify patterns and outliers, and translate findings into actionable model improvements • Experience in computational lithography, optical modeling, or image processing is a strong plus • Background working on large, complex software projects with multiple contributors and long product lifecycles is a strong plus Who You Are • You can take a vague customer complaint about model accuracy, dig into the data, isolate the root cause, and propose a fix that addresses the underlying issue without breaking existing workflows • You know when to optimize for speed and when to optimize for clarity, and you can defend that tradeoff to a senior engineer or a product manager without hand-waving • You are comfortable presenting technical results to a mixed audience, whether that is walking a field engineer through a calibration workflow or explaining a convergence failure to a PhD researcher • You do not get stuck when the data is messy or the requirements are incomplete, you make progress with what you have and course-correct as you learn more • You care about the craft of writing maintainable code, not just code that works today, and you leave the codebase better than you found it • You ask questions that cut to the core of a problem, and you listen carefully to the answers, especially when they come from people with different expertise than yours The Team You'll Be Part Of You will join the Proteus R&D team within the EDA Group, focused on computational lithography modeling for leading-edge semiconductor manufacturing. This is a collaborative, technically deep team working on problems at the intersection of physics, mathematics, and high-performance software engineering. The team works closely with cross-functional groups including product engineering, field support, and customers to deliver modeling solutions that enable next-generation chip manufacturing. You will have the opportunity to learn deeply within specific modeling topics while gaining broad exposure to new technologies across the computational lithography domain. Rewards and Benefits We offer a comprehensive range of health, wellness, and financial benefits to cater to your needs. Our total rewards include both monetary and non-monetary offerings. Your recruiter will provide more details about the salary range and benefits during the hiring process.