Postdoctoral Researchers in Neural-Symbolic Methods Scientific Computing

The Information Sciences Group (CAI-3) in the Computing and Artificial Intelligence Division at Los Alamos National Laboratory is recruiting postdoctoral researchers to develop neural-symbolic methods that automatically construct, verify, and adapt numerical solvers for time-dependent partial differential equations. The research will couple generative program synthesis with numerical and symbolic verification to produce explicit operator-splitting schemes with checkable measures of stability, accuracy, and conservation.

The Information Sciences Group (CAI-3) in the Computing and Artificial Intelligence Division at Los Alamos National Laboratory is recruiting postdoctoral researchers to develop neural-symbolic methods that automatically construct, verify, and adapt numerical solvers for time-dependent partial differential equations. The research will couple generative program synthesis with numerical and symbolic verification to produce explicit operator-splitting schemes with checkable measures of stability, accuracy, and conservation.

The successful candidates will join a multidisciplinary team spanning numerical analysis, scientific machine learning, computational physics, dynamical systems, and large-scale scientific computing. The project will progress from smooth PDE systems to shock-dominated conservation laws and multiphysics problems, including compressible flow and magneto hydrodynamics. Methods will be tested on public scientific-machine-learning benchmarks and on computational kernels relevant to Los Alamos applications.

We are particularly interested in candidates with strong foundations in numerical methods for PDEs who want to work at the interface of scientific computing and machine learning. Depending on background, candidates may contribute to operator splitting, conservative and shock-capturing discretizations, generative models for symbolic programs, verifier-guided optimization, or formal certification of numerical algorithms. Experience in every area is not required; we value deep expertise in one area and a clear interest in learning across disciplines.

• develop and analyze global and spatially local operator-splitting algorithms for nonlinear PDEs, including shock-dominated and multiphysics systems;
• build generative proposers for symbolic solver programs using methods such as autoregressive models, discrete generative models, policy optimization, and tree search;
• develop numerical and symbolic verification tools for conservation laws, entropy consistency, stability, positivity, interface fluxes, and structural admissibility;
• implement reliable research software and run numerical experiments on large-scale computing platforms;
• design reproducible benchmarks that compare the proposed methods with classical numerical solvers, physics-informed models, neural operators, and related scientific-machine-learning baselines;
• publish original research, release research software when appropriate, and collaborate with scientists at Los Alamos and partner institutions.

• PhD in applied or computational mathematics, computer science, computational physics, engineering, or a related quantitative discipline, completed within the last 5 years or to be completed soon.
• Demonstrated research experience in numerical methods for PDEs, such as time integration, finite-volume, finite-difference, or finite-element methods, operator splitting, conservation laws, or computational fluid dynamics.
• Strong programming skills in one or more languages used for scientific computing, such as Python, C++, Julia, or Fortran.
• Experience implementing, testing, and evaluating numerical algorithms beyond coursework or classroom projects.
• Evidence of research accomplishment in numerical analysis, scientific computing, scientific machine learning, or a closely related field through publications, presentations, research software, or substantial projects.
• Ability to work independently and collaboratively in a multidisciplinary scientific environment.
• Strong interpersonal, written, and oral communication skills.

• Experience with operator splitting, conservative or shock-capturing methods, adaptive or multirate time integration, magneto hydrodynamics, multiphysics, or multiscale simulation.
• Experience with scientific machine learning or generative modeling for structured or discrete objects, including reinforcement learning, Monte Carlo tree search, neural operators, or discrete-state…