Mathematical Modeling Engineer - Platform Architecture Cupertino,California,United States Hardware Exploratory Design, part of Platform Architecture, is seeking to fill a position in technology exploration, physics modeling, and numerical optimization. Exploratory Design helps Apple by building hardware prototypes that demonstrates the possibility of technological approaches that would otherwise be too risky to include in our product roadmaps. We work in a wide variety of technical fields and compare disparate ways of approaching the same challenge. **Description** For this role, we are looking for a candidate that will be well-versed in a broad range of mathematical techniques used to simulate and optimize physical systems. You will help investigate multiple alternative ways of reaching customer-focused end goals through a quantitative exploration of potential approaches. Further, you will also need to possess the following; • Ability to drive technical investigations into the feasibility of alternative approaches to problems and help us sort the impossible from the feasible. • Ability to communicate with a team that has highly diverse technical backgrounds and tune the level of technical detail they present. • Ability to thrive in an environment where goals and approaches fluctuate rapidly. **Minimum Qualifications** + BS and a minimum of 3 years relevant industry experience. + Experience with numerical simulation and optimization in at least in one of C, C++, Python, or MATLAB. **Key Qualifications** **Preferred Qualifications** + Ph.D. or equivalent in mathematical modeling, mathematical physics, mathematical engineering, or a similar field. + Understanding of physics and how to numerically simulate physical phenomena. + Command of multiple techniques in convex and non-convex numerical optimization. + Experience in simulations involving computational Physics. + Ability to choose and conduct appropriate statistical analyses to support scientific inferences. + Use of cutting edge techniques in high performance computing. **Education & Experience** **Additional Requirements** **Pay & Benefits** + At Apple, base pay is one part of our total compensation package and is determined within a range. This provides the opportunity to progress as you grow and develop within a role. The base pay range for this role is between $143,100 and $264,200, and your base pay will depend on your skills, qualifications, experience, and location.Apple employees also have the opportunity to become an Apple shareholder through participation in Apple’s discretionary employee stock programs. Apple employees are eligible for discretionary restricted stock unit awards, and can purchase Apple stock at a discount if voluntarily participating in Apple’s Employee Stock Purchase Plan. You’ll also receive benefits including: Comprehensive medical and dental coverage, retirement benefits, a range of discounted products and free services, and for formal education related to advancing your career at Apple, reimbursement for certain educational expenses — including tuition. Additionally, this role might be eligible for discretionary bonuses or commission payments as well as relocation.Learn more (https://www.apple.com/careers/us/benefits.html) about Apple Benefits.Note: Apple benefit, compensation and employee stock programs are subject to eligibility requirements and other terms of the applicable plan or program. + Apple is an equal opportunity employer that is committed to inclusion and diversity. We take affirmative action to ensure equal opportunity for all applicants without regard to race, color, religion, sex, sexual orientation, gender identity, national origin, disability, Veteran status, or other legally protected characteristics.Learn more about your EEO rights as an applicant. (https://www.eeoc.gov/sites/default/files/2023-06/22-088\_EEOC\_KnowYourRights6.12ScreenRdr.pdf) **Apple Footer** Apple is an equal opportunity employer that is committed to inclusion and diversity. We take affirmative action to ensure equal opportunity for all applicants without regard to race, color, religion, sex, sexual orientation, gender identity, national origin, disability, Veteran status, or other legally protected characteristics. Learn more about your EEO rights as an applicant (Opens in a new window) . Apple will not discriminate or retaliate against applicants who inquire about, disclose, or discuss their compensation or that of other applicants. United States Department of Labor. Learn more (Opens in a new window) . Apple participates in the E-Verify program in certain locations as required by law. Learn more about the E-Verify program (Opens in a new window) . Apple is committed to working with and providing reasonable accommodation to applicants with physical and mental disabilities. Reasonable Accommodation and Drug Free Workplace policy Learn more (Opens in a new window) . Apple is a drug-free workplace. Reasonable Accommodation and Drug Free Workplace policy Learn more (Opens in a new window) . Apple will consider for employment all qualified applicants with criminal histories in a manner consistent with applicable law. If you’re applying for a position in San Francisco, review the San Francisco Fair Chance Ordinance guidelines (opens in a new window) applicable in your area. It is unlawful in Massachusetts to require or administer a lie detector test as a condition of employment or continued employment. An employer who violates this law shall be subject to criminal penalties and civil liability.