1

Partial Differential Equations Jobs (NOW HIRING)

Deep knowledge of differential equations, numerical methods, linear algebra applications, optimization, mathematical modeling, Fourier analysis, partial differential equations, and complex analysis.

Deep knowledge of differential equations, numerical methods, linear algebra applications, optimization, mathematical modeling, Fourier analysis, partial differential equations, and complex analysis.

Deep knowledge of differential equations, numerical methods, linear algebra applications, optimization, mathematical modeling, Fourier analysis, partial differential equations, and complex analysis.

Applied Mathematics Tutor

OR · Remote

$18 - $40/hr

Deep knowledge of differential equations, numerical methods, linear algebra applications, optimization, mathematical modeling, Fourier analysis, partial differential equations, and complex analysis.

Deep knowledge of differential equations, numerical methods, linear algebra applications, optimization, mathematical modeling, Fourier analysis, partial differential equations, and complex analysis.

Deep knowledge of differential equations, numerical methods, linear algebra applications, optimization, mathematical modeling, Fourier analysis, partial differential equations, and complex analysis.

next page

Showing results 1-20

Partial Differential Equations information

See salary details

$22

$24

$26

How much do partial differential equations jobs pay per hour?

As of Jul 28, 2026, the average hourly pay for partial differential equations in the United States is $24.76, according to ZipRecruiter salary data. Most workers in this role earn between $23.80 and $25.72 per hour, depending on experience, location, and employer.

What jobs use partial differential equations?

Jobs that use partial differential equations include roles in engineering, physics, applied mathematics, and computational modeling. These professionals often work in research, simulation, and data analysis, utilizing PDEs to solve complex problems in areas such as fluid dynamics, heat transfer, and financial modeling.

What are the top 5 math careers that pay well?

For careers related to partial differential equations, high-paying options include roles such as quantitative analyst, data scientist, operations researcher, applied mathematician, and computational scientist. These positions often require strong analytical skills, proficiency in programming and mathematical modeling, and advanced degrees like a master's or Ph.D. in mathematics or related fields. Salaries vary by industry and experience but are generally above average for STEM careers.

What is a Partial Differential Equations job?

A Partial Differential Equations (PDE) job involves researching, analyzing, and solving equations that describe physical phenomena such as heat flow, fluid dynamics, and wave propagation. Professionals in this field work in academia, engineering, finance, and scientific research, using mathematical models to solve complex real-world problems. Typical roles include applied mathematicians, computational scientists, and engineers specializing in numerical simulations and modeling.

What majors take partial differential equations?

Partial differential equations are commonly studied in majors such as mathematics, applied mathematics, physics, engineering, and computational science. These fields often require knowledge of PDEs for modeling and problem-solving, and students may learn to use mathematical software tools like MATLAB or Mathematica. A strong foundation in calculus and linear algebra is typically necessary for understanding PDEs in these majors.

What are the uses of partial differential equations in real life?

Partial differential equations (PDEs) are used by professionals in fields like engineering, physics, and applied mathematics to model phenomena such as heat transfer, fluid flow, electromagnetic fields, and structural analysis. Solving PDEs helps in designing systems, predicting behavior, and optimizing processes in various industries.

What are the key skills and qualifications needed to thrive in the Partial Differential Equations position, and why are they important?

To excel in a role specializing in Partial Differential Equations (PDEs), you need a solid background in advanced mathematics or applied mathematics, often supported by a graduate degree such as a Master's or Ph.D. in mathematics, physics, or engineering. Expertise with mathematical modeling software like MATLAB, Mathematica, or COMSOL and familiarity with programming languages such as Python or C++ are typically required. Strong analytical thinking, attention to detail, and the ability to communicate complex results to both technical and non-technical team members are crucial soft skills. These competencies enable professionals to solve intricate real-world problems and collaborate effectively in research or industry project teams.

What types of industries or projects typically employ specialists in Partial Differential Equations?

Specialists in Partial Differential Equations are often employed across a broad spectrum of industries, including aerospace, engineering, finance, data science, and environmental science. They work on projects such as modeling fluid dynamics for aircraft design, simulating heat transfer in manufacturing, analyzing financial derivatives, or forecasting weather patterns. Daily responsibilities often involve collaborating with multidisciplinary teams, translating real-world phenomena into mathematical models, and developing computational solutions. Working in this field offers opportunities to contribute to innovative research and applied solutions, with clear pathways for advancement into senior research, technical leadership, or academic positions.

More about Partial Differential Equations jobs
What are the most commonly searched types of Partial Differential Equations jobs? The most popular types of Partial Differential Equations jobs are:
Infographic showing various Partial Differential Equations job openings in the United States as of July 2026, with employment types broken down into 1% As Needed, 76% Full Time, 20% Part Time, and 3% Nights. Highlights an 94% Physical, 1% Hybrid, and 5% Remote job distribution, with an average salary of $51,500 per year, or $24.8 per hour.
Machine Learning Physics Graduate Student

Machine Learning Physics Graduate Student

LLNL

Livermore, CA • On-site

$6.7K - $8.2K/mo

Full-time

Retirement

Posted 26 days ago


Job description

Company Description
Join us and make YOUR mark on the World!
Lawrence Livermore National Laboratory (LLNL) has turned bold ideas into world-changing impact advancing science and technology to strengthen U.S. security and promote global stability.
Our mission spans four critical national security areas nuclear deterrence, threat preparedness, energy security, and multi-domain defense empowering teams to take on the toughest challenges of today and tomorrow. With a culture built on innovation and operational excellence, LLNL is a place where your expertise can make a real impact.
Job Description
We have multiple openings for Machine Learning Graduate Student Interns to engage in practical research experience to further their educational goals. You will work on multidisciplinary projects, such as development of classical empirical and machine learning interatomic potentials, discovery of partial differential equations (PDEs), numerical solutions of partial differential equations to model material behavior at continuum scale and analysis of large atomic datasets. These positions are in in the Equation of State Materials Theory Group of the Physics Division of the Physical & Life Sciences Directorate.
This position requires full-time on-site presence due to the nature of the work.
You will
  • Develop parallel C/C++/Python codes to train, test and evolve (a) PDEs (for phase field and phase field crystal models) discovered from data, and (b) interatomic potentials developed from quantum simulations.
  • Explore the use of machine learning methods to discover and evolve PDEs for phase field and phase field crystal models.
  • Analyze results, provide weekly updates and present work at poster sessions
  • Review literature in the field of study, document results and write papers.
  • Perform other duties as assigned.

Qualifications
  • Must be eligible to access the Laboratory in compliance with Section 3112 of the National Defense Authorization Act (NDAA). See Additional Information section below for details.
  • Continuing student in good standing at an accredited institution of higher education pursuing a graduate degree in Physics or related field.
  • Research background with a record of publication.
  • Experience in writing codes (in C/C++ and Python) and a background in Materials Science/Engineering/Physics/Applied Mathematics.
  • Excellent skills in written and verbal communication, as well as teamwork.

Qualifications We Desire
  • Experience in parallel computing, porting codes to GPUs, experience in numerical solutions of partial differential equations.

Pay Range
$6,752 - $8,201 Monthly
This position is under a step structure. Please note that the step placement is determined by your most recent completed academic year.
Additional Information
#LI-Onsite
Why Lawrence Livermore National Laboratory?
  • Included in 2026Best Places to Work by Glassdoor!
  • Holiday Pay
  • Sick leave accrual
  • Individual 401(k) contributions
  • Our values - visit https://www.llnl.gov/inclusion/our-values

Security Clearance
None required.However, if your assignment is longer than 179 days cumulatively within a calendar year, you must go through the Personal Identity Verification process. This process includes completing an online background investigation form and receiving approval of the background check.
National Defense Authorization Act (NDAA)
The 2025 National Defense Authorization Act (NDAA), Section 3112, generally prohibits citizens of China, Russia, Iran and North Korea without dual US citizenship or legal permanent residence from accessing specific non-public areas of national security or nuclear weapons facilities. The restrictions of NDAA Section 3112 apply to this position. To be qualified for this position, Candidates must be eligible to access the Laboratory in compliance with Section 3112.
Pre-Employment Drug Test
External applicant(s) selected for this position must pass a post-offer, pre-employment drug test. This includes testing for use of marijuana as Federal Law applies to us as a Federal Contractor.
Wireless and Medical Devices
Per the Department of Energy (DOE), Lawrence Livermore National Laboratory must meet certain restrictions with the useand/or possession ofmobile devices in Limited Areas. Depending on your job duties, you may be required to work in a Limited Area whereyou are not permitted to have a personal and/or laboratory mobile devicein your possession. This includes, but not limited to cell phones, tablets, fitness devices, wireless headphones, and other Bluetooth/wireless enabled devices.
Ifyou useamedical device, whichpairs with a mobile device,you must still follow the rules concerningthe mobile device in individual sections within Limited Areas. Sensitive Compartmented Information Facilities requireseparate approval. Hearing aids without wireless capabilities or wireless that has been disabled are allowed in Limited Areas, Secure Space and Transit/Buffer Space within buildings.
How to identify fake job advertisements
Please be aware of recruitment scams where people or entities are misusing the name of Lawrence Livermore National Laboratory (LLNL) to post fake job advertisements. LLNL never extends an offer without a personal interview and will never charge a fee for joining our company. All current job openings are displayed on the Career Page under "Find Your Job" of our website. If you have encountered a job posting or have been approached with a job offer that you suspect may be fraudulent, we strongly recommend you do not respond.
To learn more about recruitment scams: https://www.llnl.gov/sites/www/files/2023-05/LLNL-Job-Fraud-Statement-Updated-4.26.23.pdf
Equal Employment Opportunity
We are an equal opportunity employer that is committed to providing all with a work environment free of discrimination and harassment. All qualified applicants will receive consideration for employment without regard to race, color, religion, marital status, national origin, ancestry, sex, sexual orientation, gender identity, disability, medical condition, pregnancy, protected veteran status, age, citizenship, or any other characteristic protected by applicable laws.
Reasonable Accommodation
Our goal is to create an accessible and inclusive experience for all candidates applying and interviewing at the Laboratory. If you need a reasonable accommodation during the application or the recruiting process, please use our online form to submit a request.
CaliforniaPrivacy Notice
The California Consumer Privacy Act (CCPA) grants privacy rights to all California residents. The law also entitlesjob applicants, employees, and non-employee workers to be notified of what personal information LLNL collects and for what purpose. The Employee Privacy Notice can be accessed here .