Math & Physical Sciences

Compute coordinates, read FITS files and run cosmology math with Astropy

Balance reactions, run thermodynamics and query PubChem for molecular data

Check solution convergence with Richardson extrapolation and Grid Convergence Index

Download ERA5 reanalysis, climate projections and satellite climate data from CDS

Model solar, wind and battery storage with techno-economic analysis

Analyze climate, pollution and biodiversity data for environmental studies

Run Python fluid simulations of Navier-Stokes, shallow water and turbulent flows

Prove theorems and check formal proofs with the Lean 4 prover

Pick direct or iterative linear solvers and fix GMRES, CG and BiCGSTAB stalls

Query Materials Project for crystal structures, band gaps and stability data

Analyze alloy, ceramic and polymer properties with phase diagrams and characterization

Screen materials for batteries, catalysts and semiconductors by property and stability

Solve equations, integrals and differential equations with Python numerical tools

Plan mesh resolution, aspect ratios and adaptive refinement for PDE simulations

Run molecular dynamics with OpenMM and analyze trajectories and binding

Pick Newton, BFGS or Broyden solvers and diagnose nonlinear convergence

Choose time integration schemes and error tolerances for ODE and PDE simulations

Check CFL limits, von Neumann stability and stiffness in PDE simulations

Tune simulation parameters with design of experiments and sensitivity analysis

Solve classical, quantum and thermodynamics problems with derivations and unit checks

Extract and visualize simulation output with time series and report generation

Search PubChem for compound properties, structures and similarity matches

Build crystal structures, phase diagrams and VASP input with pymatgen

Design quantum circuits, algorithms and error-correction plans

Work with SMILES, molecular properties and fingerprints using RDKit

Forecast next-day hourly electricity load for buildings from smart-meter history

Forecast next-day global temperature fields on an ERA5-style grid

Forecast dissolved oxygen and water temperature 30 days ahead with uncertainty

Decide satisfiability of nonlinear integer SMT-LIB formulas as sat, unsat or unknown

Predict phonon peak frequencies of inorganic crystals from their structure

Work through mathematical and physical problems with formal proof construction

Run FFT spectral analysis, digital filters and noise reduction on signals

Run parameter sweeps and batch simulation campaigns, then aggregate results

Check simulations for NaN, convergence and conservation before and after runs

Solve equations, do calculus and manipulate symbolic math with SymPy

Set time-step policies that respect CFL limits and schedule outputs for simulations