PhD: Designing ensembles for efficient climate model emulation and uncertainty quantification

PhD: Designing ensembles for efficient climate model emulation and uncertainty quantification

Research Question and Application Judgment

This Exeter project asks how to choose expensive climate simulations so that a statistical emulator learns efficiently across uncertain parameters and emissions trajectories. Its attraction is a direct connection between the advertised problem and Peter Challenor and Hossein Mohammadi's original work on Gaussian processes, adaptive designs and dynamical emulation. International students can compete for an award covering international tuition, but places are limited and individual academic eligibility remains conditional.

The UNRISK timetable lists 16 November 2026 as the opening date and 13 January 2027 at 13:00 GMT as the 2027-entry deadline. Do not confuse the opening date with the cutoff or use superseded Leeds application codes. Prepare by clarifying the starting simulator, design objective and host admission route, then confirm the updated instructions and portal availability when submitting. Application process Opening warning

Research Problem and Doctoral Work

Climate simulations are expensive, while a small collection of socioeconomic pathways cannot describe every plausible emissions trajectory. The project description proposes representing trajectories as mathematical curves and building statistical emulators, including Gaussian processes, over emissions and parameter uncertainty. Sequential experimental design would choose additional runs to improve information gained per computational cost. The exact climate model, trajectory representation, output resolution and computing allocation have not been specified.

The statistical problem is consequential: a fast surrogate is useful only within a domain supported by its simulations and assumptions. Emulator uncertainty concerns approximation of a simulator; it does not automatically include structural climate-model error, internal variability or uncertainty about future human choices. Expanding the input space can also make a nominally efficient method impractical. These distinctions should shape the thesis before a policy-facing tool is promised.

A manageable research sequence could establish a reproducible baseline on a tractable simulator, compare fixed and adaptive designs under equal budgets, and then extend the method to a defined family of emissions curves. This is an analytical suggestion, not an assigned work package. Evaluation should examine held-out prediction, interval calibration, acquisition overhead and where runs are placed, alongside average error. A design intended for global accuracy may allocate simulations differently from one targeting extremes or a decision threshold.

For context, Beusch and colleagues' 2022 MAGICC–MESMER paper connects emissions pathways to spatial annual temperature fields and represents forced-response and natural-variability uncertainty. The cited abstract and publication record describe external field work, not a study by this project's supervisors or a confirmed model for the student. A useful doctorate might deliver a validated design method, a reproducible comparison or a defensible uncertainty representation without establishing an operational policy system. External climate-emulator study

The most important feasibility question is whether new simulations can actually be commissioned. If only a fixed historical ensemble is available, evaluating sequential design requires an agreed retrospective or smaller-model strategy. Curve constraints, physical plausibility and reserved validation runs also matter: reducing the number of expensive runs is meaningful only if the resulting predictions remain credible.

School, Programme and Field Context

The project description identifies University of Exeter, Mathematics and Statistics as host. The university's postal address explicitly places it in the UK. UNRISK states that students register for a PhD at one of its three universities; Leeds manages the common recruitment administration. For this Exeter project, the intended degree institution is Exeter, subject to its later formal admission. Completing the Leeds administrative form does not imply a Leeds award or joint degree. Exact registration title and final supervisory appointments need confirmation. University location Training structure

Exeter's Statistics and Data Science group explicitly works on computer-model calibration and uncertainty quantification and lists both named researchers. Its Weather and Climate Science group describes probabilistic projections, statistical emulation and strong Met Office links. These are relevant disciplinary resources, not evidence of a project-specific Met Office placement or guaranteed access to its models. The IDSAI uncertainty theme names Challenor and Danny Williamson as leads, supporting a wider methodological setting. Statistics group Climate group IDSAI uncertainty theme

The university's current rankings page reports QS 2027 global rank 136 and THE 2027 joint 157. These overall positions provide institutional context. The department separately reports internationally excellent mathematical-sciences research impact in REF 2021; that impact measure is not a current subject ranking or supervision score. Departmental seminars, workshops and interdisciplinary institutes are more directly connected to training. University rankings Departmental research

UNRISK combines research from the beginning with cohort events concentrated in the first half-year, residential workshops and unassessed specialist modules. Topics span at least two of climate science, data science and decisions; every student has at least two academic supervisors. Cohort activities do not themselves count toward the doctoral award. The advertised funding period is three years nine months, including an expected three-month placement; this is not a guarantee of completion or funding for every writing-up circumstance.

Supervisors and Recent Original Research

Challenor's official profile describes carefully designed runs and Gaussian-process surrogates for expensive numerical models, with applications in prediction, sensitivity, calibration and uncertainty analysis. It also identifies him as PI of EXA-UQ concerning next-generation high-performance computing. This supports relevant expertise, but does not establish an allocation of that project's compute to this studentship. Mohammadi's official profile identifies him as Lecturer in Statistics and Data Science, researching GP emulation, adaptive computer experiments, Bayesian optimisation and uncertainty analysis for climate and environmental prediction. Challenor Mohammadi

Adaptive design for costly computer codes

Mohammadi and Challenor's Sequential adaptive design for emulating costly computer codes, DOI 10.1080/00949655.2024.2436013, appeared online in December 2024 and in the 2025 journal volume. The methods summary refers to the March 2024 author-manuscript version, not the publisher's final text. Its VIGF criterion combines GP uncertainty with discrepancy from the nearest observed response; batch sampling discourages nearby selections, and hierarchical kriging extends the design to two fidelity levels.

Eight benchmarks, including circuit and piston problems, were compared using repeated designs and normalised prediction error. The reported gains vary by function; neither universal dominance nor success on a full climate model follows. The nearest-point geometry and tested low-to-medium dimensions raise questions for high-dimensional curve inputs. Mohammadi is the listed corresponding author and Challenor the coauthor; no individual coding or theoretical task allocation was established. Methods and results, author manuscript Version history

Emulating dynamical trajectories

Mohammadi, Challenor and Goodfellow's Emulating Complex Dynamical Simulators with Random Fourier Features was published in SIAM/ASA Journal on Uncertainty Quantification in 2024, DOI 10.1137/22M147339X. Its current author manuscript fits a GP to a short-time flow map and approximates function draws with random Fourier features. Reusing each sampled map through successive steps creates a distribution of trajectories, preserving uncertainty propagation rather than just repeating point predictions.

Tests include Lorenz, van der Pol and Hindmarsh–Rose systems. The paper reports improved trajectory prediction compared with the earlier method, while acknowledging a predictability horizon: uncertainty can widen after accurate trajectory tracking fails. Most studied systems are two- or three-dimensional, with further high-dimensional investigation needed. This is relevant groundwork, not validation of arbitrarily long climate projections. Mohammadi is listed as corresponding author; individual contributions cannot be inferred from author order alone. Author manuscript, methods and selected results Journal identification and versions

Learning where an emulator is wrong

Mohammadi, Challenor, Williamson and Goodfellow's 2022 Cross-Validation–based Adaptive Sampling for Gaussian Process Models, DOI 10.1137/21M1404260, models expected squared leave-one-out error with a second GP and uses a repulsion-modified acquisition rule to avoid clustered selections. A batch extension allows several runs to be selected together. The methods, experiments and conclusions summarized here are based on the October 2021 v6 author manuscript; publication information records online publication in February 2022 and the March issue.

The experiments compare analytic functions and circuit/piston problems. Fixed Latin hypercube designs perform strongly on some analytic tests; adaptive selection offers a stopping advantage and better behaviour on the tested physical examples. The authors explicitly leave asymptotic convergence proof unresolved. A second GP also creates overhead that matters when simulator costs are moderate. Both proposed supervisors are authors, alongside Williamson and Goodfellow; specific personal tasks remain unknown. Author manuscript Published record

Together these three original studies establish a coherent methodological programme. They do not determine the student's eventual acquisition function. Agreement on diagnostic tests, supervision frequency, climate-domain support and realistic computational budgets is more useful than treating every related paper as an assigned technique.

Funding, Application and Living Cost

Current UNRISK funding information promises full tuition, including international fees, for successful scholarship recipients. It provides a standard UKRI stipend for three years nine months, an expected three-month placement, £6,000 individual RTSG and £5,000 per-student cohort training support. These research/training budgets are not extra living cash. The applicable 2027/28 stipend amount was not established, so no annual disposable-income forecast is justified. The page's cumulative 40-student and 12–15-per-cohort figures are older scheme wording, not a verified 2027 quota. Funding conditions

The 2027 project browser instead expects 18 recruits from 38 advertised projects, while noting that descriptions are still being uploaded. Not every advertised project is guaranteed its own funded student. International awards are limited and highly competitive. The FAQ explicitly remains applicable to 2027, subject to timing changes, and confirms fee-difference coverage while excluding relocation, travel, visa and health-surcharge costs. Its £3,000–£4,000 immigration estimate is indicative scheme wording, not a personalised current invoice. 2027 browser Current FAQ applicability

Exeter's April 2026 budgeting guidance estimates £1,300–£2,000 a month for a single student, including rent and ordinary expenses. Annualising that range gives approximately £15,600–£24,000 for twelve months, before separately planned arrival and immigration expenses. Housing choice and whether bills are included materially affect the budget. A stipend comparison should wait for the correct entry-year amount. Living-cost guidance

The university and current government visa page state £1,171 monthly outside London for up to nine months, or £10,539. This is an immigration maintenance calculation, not an annual doctorate budget. The government lists China under differential evidence requirements, but may still request evidence; this does not remove the need to have sufficient funds or establish individual visa eligibility. University visa-cost context Government financial requirement

A process notice says the detailed instructions below its banner describe the 2026 process and that 2027 instructions were expected in late October; whether updated guidance has since appeared is unconfirmed. The common framework uses both Leeds OLA and an UNRISK form even for Exeter. Existing structured-CV questions and document guidance are useful preparation, but word limits, codes and submission instructions must be checked against the 2027 update.

Applicant Background and China Eligibility

The project seeks mathematics, statistics, data science or another highly quantitative background, such as physics or theoretical computer science. Experience or strong interest in GPs, uncertainty quantification, active learning and climate simulation is desirable. These are project-specific preferences; they should not be rewritten as a requirement to have mastered every method before entry.

UNRISK's minimum is a relevant 2:1 honours degree or equivalent, with non-UK equivalents accepted. A master's is not a uniform CDT requirement. Applicants already awarded a PhD or currently registered for one are excluded; previous incomplete doctoral study may be considered. This creates an explicit international application and funding path for Chinese applicants, conditional on individual assessment.

Exeter's China page nevertheless says research applicants generally complete a three-year Chinese master's with diploma and degree certificate. Its taught-postgraduate percentage table is not a doctoral threshold. The CDT minimum and host guidance must therefore be reconciled by admissions, particularly for Chinese bachelor's-only applicants or a different master's duration. The page's CSC partnership concerns a separate scheme and is not assumed to be linked or stackable. China research-entry guidance

The CDT links Exeter's Profile A English page, currently IELTS 6.0 overall and at least 6.0 in each component. The final department and offer should confirm the applicable profile and accepted evidence. English proof need not be completed by the CDT application deadline, but must satisfy registration conditions; the CDT says tests must be within two years at the start. This is not an automatic waiver. Linked English profile

Suggested preparation is a reproducible comparison of a space-filling design and a sequential design on a public simulator, including held-out error, interval coverage, runtime and a candid failure analysis. Coding in R or Python, linear algebra, probability and numerical modelling provide a useful foundation. These suggestions are not additional admission conditions. A machine-learning portfolio that reports accuracy alone would leave the project's central uncertainty question unanswered; a climate portfolio without quantitative evidence would need to address the advertised statistical emphasis.

Career Outlook

UNRISK identifies climate-service organisations, operational prediction centres, consultancies, financial and reinsurance advisers, public bodies and humanitarian organisations as relevant destinations. The transferable contribution is statistical reasoning about expensive models and communicating what their uncertainty permits. These are plausible routes, not project-specific graduate placements or salary promises. The funded placement may help explore a sector, but its host has not been identified for this student. Career context

Next Actions and Questions to Verify

Before submission, confirm the 2027 instructions and personal portal availability; the timetable lists 16 November as the opening date. Confirm the precise host registration, final supervisory team, individual Chinese qualification interpretation and English profile. The project description names Exeter, Challenor, Mohammadi and UNRISK.

At interview, establish the first simulator and input representation, whether the objective is global fit or decision-relevant risk, and the budget for commissioning and validating runs. Ask how model discrepancy and internal variability will remain separate from emulator error, and what fallback is available if expensive new simulations cannot be generated. Confirm day-to-day guidance and who supplies climate expertise.

Before acceptance, obtain the entry-year stipend and funded-period terms, fee coverage, placement expectations and any writing-up gap in writing. Build a twelve-month housing and arrival budget, and clarify immigration evidence with the university. The principal decision is whether a well-scoped statistical thesis can be supported by actual simulator access and a competitive funded offer, rather than whether a fast surrogate alone can promise climate-policy impact.

Evidence and Sources

The timetable lists 16 November 2026 as the opening date and 13 January 2027 at 13:00 GMT as the deadline; neither date establishes current portal availability. The available guidance still includes 2026 wording and codes, so confirm the 2027 instructions before applying. The cited supervisor studies report results on specified benchmark functions and low-dimensional dynamical systems, not on this project’s climate simulator; the MAGICC–MESMER record provides abstract-level field context.

• Recruitment and funding: Opening warning, application timetable, requirements and funding, 2027-valid FAQ, project-browser boundary.
• School and training: University location, UNRISK training, statistics, weather and climate, IDSAI uncertainty, department, rankings.
• Supervisors and originals: Challenor, Mohammadi, VIGF methods, VIGF versions, RFF manuscript, RFF journal identification, ES-LOO manuscript, ES-LOO published record.
• Applicant and cost: China guidance, English, living budget, university immigration-cost context, government maintenance.
• Field and careers: external MAGICC–MESMER study, abstract-level context, UNRISK careers.