Selected research in numerical simulation, inverse problems and scientific machine learning, with methods and evaluation in each case study.
Research projects
5 projects
Thin-structure diagnostic · 50 images per pointInverse problems · Imaging
Sparse-view photoacoustic reconstruction
Testing when a learned reconstruction beats model-based inversion, and why it fails under distribution shift.
Synthetic inverse problem comparing Tikhonov inversion with learned reconstruction. A network far ahead on its training image families fell behind on unseen thin structures, and two preregistered experiments tested why.
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Research figure · open case study for contextScientific ML · Model reduction
Reduced models & neural operators
Comparing fast approximations of nonlinear transport.
Compared classical and learned PDE surrogates: POD achieved 0.152% relative L² error versus 0.90% for FNO on 40 in-distribution cases (five FNO seeds).
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Research figure · open case study for contextDynamical systems · Uncertainty
Data assimilation for chaotic Lorenz-96
Estimating chaotic system states from noisy observations.
In a 10-seed study with a selected localisation radius, reduced state-estimation RMSE from 4.63 to 0.41 using Ensemble Kalman filtering.
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Research figure · open case study for contextM.Sc. thesis · Applied mathematics
Optimal mixing of passive scalars
Reproducible pseudo-spectral study of optimal passive-scalar mixing.
Extended M.Sc. thesis computations to N=512 with 48 verification tests; established approximately second-order convergence of fixed-window exponent fits.
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Research figure · open case study for contextCFD · Finite elements
Finite-element cylinder-flow benchmarks
Measuring solver accuracy on standard cylinder-flow problems.
Taylor–Hood finite-element solver verified at O(h³)/O(h²) velocity convergence, with steady cylinder-flow results closely matching the published reference.
Read case study →Generative AI & LLM Applications
Retrieval-augmented generation systems developed with explicit evaluation of retrieval quality, evidence grounding and failure modes. These are research implementations, not claims of production deployment.
Multimodal RAG · Document understanding
Multimodal Visual RAG ↗
Question answering over document pages containing text, tables, charts and images.
Compares OCR-based keyword and dense retrieval with image embeddings, hybrid fusion and reranking; evaluates answer grounding, page citations and abstention. On the documented textbook corpus, text hybrid retrieval was a strong baseline and visual retrieval did not show a meaningful improvement. GPU experiments remain separately pending.
Research evaluation · corpus-specific results
Methods, results and limitations ↗Legal RAG · Citation verification
Legal Research RAG ↗
Source-grounded case-law retrieval and research summaries with citation checks.
Evaluates BM25, dense and hybrid retrieval, reranking, jurisdiction and date constraints, citation support and abstention. On 2,000 test queries, BM25 reached nDCG@10 of 0.176; normalized-score hybrid reached 0.186. Citation existence checks worked reliably, but substantive support and abstention remain limitations.
Research implementation · not legal advice; no citator
Methods, results and limitations ↗Additional projects
Further research and engineering work; consult each repository for current evaluation status.
- Darcy inverse problem — PDE-constrained and Bayesian inversion
- Topology optimisation — finite elements and SIMP
- DSA learning portal — educational software