I work on scientific computing and machine learning for dynamical systems, with a focus on probability densities, numerical methods and data assimilation.

My current research asks how a learned forecast operator can propagate a complete probability density for the Lorenz system, and what evidence is needed before that surrogate can be trusted in Bayesian data assimilation.

Lorenz Fokker–Planck & operator learning

A research programme connecting finite-element probability-density evolution with operator-learning qualification. The numerical work includes discontinuous Galerkin methods, positivity constraints, full diffusion tensors and locally refined hexahedral meshes.

The operator-learning stage is in progress. An end-to-end neural pilot has demonstrated data-generation and GPU-training feasibility; statistical fidelity, reference applicability and surrogate qualification remain open. The eventual assimilation method is a full-density Bayesian update, without imposing a Gaussian or Gaussian-mixture state approximation.

Programme and evidence · Research integrity

These projects show the range of my work, with their evidence status made explicit. The older studies are exploratory; a code and research-quality review records limitations and proposed repairs. Listing a project here does not imply that its scientific conclusions have been independently validated.

• Lorenz datasets in C++ — trajectory-generation work, with a tested deterministic integrator proposed for review. The historical generator has correctness defects.
• Multivariate time-series analysis — Madrid air-quality exploration, with a train-only chronological baseline proposed for review. Historical scores need re-evaluation.
• Learning chaotic dynamics — historical reservoir-computing and nonlinear autoregressive experiments. Forecast alignment and out-of-sample evaluation require repair before strong comparisons.
• Bayesian data-fusion notes — Gaussian teaching examples, with a sensor-accounting correction proposed for review. Separate from the full-density formulation of the current research.

Define the scientific question. Preserve competing explanations. Test against strong baselines. Record assumptions, failed experiments and the limits of each claim.

I distinguish mathematical proof, numerical verification and empirical evidence. A successful software run is one part of the argument; application qualification requires more.

Tools across these projects: Python · C++ · Jupyter · finite elements · numerical optimisation · neural operators

Earlier repositories remain available as a research history. Their methods and conclusions should be read in the context of each experiment; they do not automatically describe the current programme.