[Hiring] PhD Research Intern, Physics-based Model Predictive Control for Thermal Systems @Phaidra

Role Description

You are a 3rd or 4th year PhD student in control, mechanical or chemical engineering, applied mathematics, machine learning, or a related field. You enjoy building models of physical systems and using them to make better decisions. You are comfortable moving between first-principles thinking, numerical optimization and practical code.

This is a paid 3-month research internship starting in January or February 2027, ideally based in the UK. You will work closely with a dedicated mentor on Phaidra's team.

The project builds on preliminary work using physics-based models to forecast thermal system dynamics over a short horizon and optimize action trajectories via model predictive control (MPC). The aim is to replace or augment purely deterministic controllers with an internal model that lets an agent look ahead. It should plan set point trajectories that anticipate load transients, thermal lags and downstream temperature constraints, rather than reacting only once they have been breached. This has already shown promise in in-rack cooling distribution unit (CDU) simulations, where a short-horizon MPC on a physics-based CDU model rejected load disturbances while respecting temperature constraints.

There is substantial room to take this further, and you are free to steer the work toward your own interests and background. Possible directions include:

• Forecast model architectures and uncertainty quantification
• Solver performance and constraint handling
• Getting an MPC controller running reliably against real hardware

The deliverable can be a paper characterizing what was learned, a piece of shipped software, or a blend of the two.

Responsibilities

• Get up to speed on the existing physics-based CDU models, simulation environment and MPC prototype, and reproduce the current in-rack CDU results.
• Extend the modeling approach to new configurations, such as end-of-row CDUs, and validate models against simulation and real telemetry.
• Investigate learned or hybrid forecast models, for example physics plus a learned residual, where pure physics models fall short.
• Improve controller robustness to model mismatch and disturbance uncertainty, and strengthen constraint handling and solver performance.
• Design and run rigorous evaluations against baseline controllers, with clear metrics for constraint satisfaction, disturbance rejection and energy use.
• Explore AI-agent workflows that automate model discovery from historical data and system documentation.
• Write clean, tested, reproducible code and document methods, assumptions and results so others can build on them.
• Communicate progress through regular check-ins, a mid-point review and a final presentation to the wider team.
• Produce a final deliverable agreed with your mentor: a paper or technical report, shipped software, or a blend of the two.

Qualifications

• Currently in the 3rd or 4th year of a PhD in control engineering, mechanical or chemical engineering, applied mathematics, machine learning, or a closely related field.
• Solid grounding in model predictive control, optimal control or trajectory optimization.
• Experience modeling dynamic physical systems, such as ODE or DAE models, heat transfer or fluid systems.
• Strong Python skills and experience with the scientific computing stack.
• Ability to design experiments, analyze results critically and communicate findings clearly in writing and in person.
• Available to start in January or February 2027 for a 3-month period, and ideally based in the UK.
• Shares our company values: Agency, Velocity, Craft, and Truth.

Preferred Skills & Experience

• Experience with optimization and MPC tooling such as CasADi, acados, do-mpc, or similar.
• Experience with system identification, grey-box modeling or physics-informed machine learning.
• Familiarity with robust, stochastic or tube MPC, or with uncertainty quantification for forecast models.
• Experience with JAX or PyTorch for differentiable or learned models.
• Background in HVAC, data centre cooling or other thermal-fluid systems.
• Experience deploying controllers on real hardware or working with noisy operational telemetry.
• Interest in using LLM-based agent workflows for scientific or engineering tasks.
• A publication record in control, optimization or machine learning venues.

Onboarding

In your first 30 days…

• Complete onboarding and gain access to the codebase, simulation tooling and relevant historical telemetry.
• Reproduce the existing in-rack CDU MPC baseline in simulation and document any gaps or issues found.
• Complete a focused literature review covering the chosen direction and relevant prior work.
• Agree a written project plan with your mentor, including the research direction, success metrics, evaluation scenarios and the target final deliverable.

In your first 60 days…

• Deliver a working first version of the core contribution, such as an end-of-row CDU model, a hybrid forecast model or a robust MPC formulation.
• Benchmark it against the baseline controller on the agreed simulation scenarios, and validate model forecasts against real telemetry where available.
• Present interim results at a mid-point review, including what is working, what is not and the plan for the final month.
• Agree with your mentor whether an extension to 6 months makes sense and, if so, what it would cover.

In your first 90 days…

• Complete the evaluation, including robustness tests under model mismatch and disturbance uncertainty, with results that are reproducible from the repository.
• Deliver the agreed final output: a paper or technical report draft, merged and documented software, or both.
• Present findings to the wider team, covering results, limitations and recommended next steps.
• Hand over code, data and documentation so the work can be continued, or set out a detailed plan for the extension period if the internship is extended.

General Interview Process

• All of our interviews are held via Google Meet, and an active camera connection is required.
• Meeting with People Operations team member (30 minutes)
• Meeting with Hiring Manager (45 minutes)
• Culture fit interview with one of Phaidra’s co-founders (30 minutes)

Base Salary

• UK Residents:
• Tier 1 (London): 45 GBP/hour
• Tier 2 (Manchester, Birmingham, Edinburgh, Bristol): 40 GBP/hour
• Tier 3 (Smaller cities / rural areas): 35 GBP/hour
• In addition to base salary, this position is eligible for equity. Final salary will be determined based on several factors, including a candidate’s qualifications, skills, competencies, experience, expertise, education and location. In some cases, final compensation may fall outside the posted range. Salary ranges are regularly reviewed and may be adjusted in response to market trends.

On being Remote

We take a thoughtful and intentional approach to remote collaboration. Inspired by pioneers like GitLab, we embrace proven best practices to foster an exceptional remote work environment. Our culture is documentation-first, and we prioritize asynchronous communication to support focus and flexibility across time zones. While we value independence, we stay closely connected through tools like Slack and video conferencing. Weekly all-hands meetings help us align and build strong relationships, and we regularly host virtual team-building activities and social events to maintain a sense of camaraderie.

Equal Opportunity Employment

Phaidra is an Equal Opportunity Employer; employment with Phaidra is governed on the basis of merit, competence, and qualifications and will not be influenced in any manner by race, color, religion, gender, national origin/ethnicity, veteran status, disability status, age, sexual orientation, gender identity, marital status, mental or physical disability, or any other legally protected status. We welcome diversity and strive to maintain an inclusive environment for all employees. If you need assistance with completing the application process, please contact us at [email protected].

E-Verify Notice

Phaidra participates in E-Verify, an employment authorization database provided through the U.S. Department of Homeland Security (DHS) and Social Security Administration (SSA). As required by law, we will provide the SSA and, if necessary, the DHS, with information from each new employee’s Form I-9 to confirm work authorization for those residing in the United States.