We aim to make it easier to integrate optimisation with on-line learning, bayesian computation and large simulation frameworks through dedicated differentiable algorithms. Our solution is suitable for both research and applications in performance demanding systems such as encountered in streaming analytics, game development and high frequency trading.

• Bayesian Computation for Deep Learning in Modern C++ [itCppCon21] [notebook]

High energy physics (HEP) beyond colliders challenges mathematical models and their implementation in a unique way. We have to take into account complex interactions with the media the experiment takes place in. This however opens up the door to answer subtle questions not only about the HEP process studied, but also the media itself.

For example, the detection of atmospheric muons passing through various obstacles leads to the development of imaging tools (muography) for their matter density, as well as a possibility to discriminate materials traversed, based on their atomic number.

Data collected from such experiments becomes significant, and the equipment is getting accessible beyond the physics labs for applications. We build a software suite  to perform Monte-Carlo simulations of particles passing through matter integrated with differentiable programming techniquess carrying out analysis and inference on that data with performance and modelling complexity suitable not only for further scientific work, but also meeting industry requirements.

• Differentiable Programming for Particle Physics Simulations,  JETP, Vol. 161 (2), (2022) [arXiv] [QUARKS-2021 conference] [notebook]

• Vectorised CSDA muon transport with GPU acceleration (2023) [notebook]

Our specific interest is in environmental control and survey tasks. Various industrial processes in geological formations, such as carbon dioxide capture sequestration, underground energy storage, enhanced oil recovery, hydraulic fracturing, well disposal, etc. could present safety and environmental risks including groundwater contamination. In the case of storage, any leaks would also be detrimental for the performance of the capture system.

This activity must be thoroughly monitored in order to avoid long-time pollution of freshwater aquifers in the subsurface.

We offer high performance solvers for inverse problems arising in monitoring systems based on hydro-thermo-mechanical-chemical data, but also muography, seismic surveys, gravimetry or inSAR.

• Differentiable Programming for MHFEM with Mass Lumping (2023) [notebook]

• Adjoint Sensitivity Method for Two-Phase Flow Model in Porous Media with Barrier Effect (2023) [notebook]

• Differentiable Model for Muon Transport and Two-Phase Flow in Porous Media with applications to Subsurface Pollution Monitoring (2022) [notebook] [EGU22 Conference] 

We build a platform incorporating differentiable programming into ab initio molecular dynamics leading to a performant high-throughput computational screening system for new materials identification. 

One important application we focus on is carbon capture technologies. Rotor & amine scrubbing are very efficient but require large installations. Membrane capturing technology is compact, absorbing CO2 at relatively low pressures and ambient temperature. Therefore, it is more convenient to use in many scenarios, such as gas leaks capturing in geological storages. 

However, improvement on membrane technology is required as only 60% effectiveness is attained as of now. This can be addressed with the design of materials that are incorporated into the membrane's core which is the challenge we are tackling with our platform.

• Adjoint Sensitivity Method for Kohn-Sham Equations  (2023) [ChemRxiv] [notebook]

We are building a derivative pricing library with a strong focus on the differentiable programming paradigm. We implement efficient algorithms for sensitivity analysis of various pricing models suitable for fast calibration in realtime trading environments, and benefiting from GPU acceleration for risk evaluation of large trading books. Yet our aim is to avoid as much as possible compromises on computational accuracy and underlying dynamics expressiveness needed in complex modelling set-ups.

We hope also that our approach will make it easier to integrate pricing components directly into algorithmic trading systems and machine learning pipelines, as well as portfolio and margin optimisation platforms.

• Computational Finance Course: 

  1.  Introduction: Arbitrage and Risk-Neutral Pricing

  2.  Black-Scholes-Merton Model

  3. Volatility Surface Calibration

• NOA-ATRA: a trading analytics platform that leverages NOA and its Kotlin frontend within the KMath library. 

• Are Cryptocurrency Markets Running Behind the Fed? A Significant Shift in Crypto Markets Microstructure (2021) [SSRN] [Press Release] 

Main interests lie in the study of singularities for geometric PDEs.

• Quantization of Time-Like Energy for Wave Maps into Spheres (2016) [arXiv] [CMP]

• Normal forms of convex lattice polytopes, with A.  Kasprzyk (2013) [arXiv]

Roland  studied  Maths at Oxford, Cambridge and Imperial. He worked in the financial industry as a quantitative developer building models for interest rates exotic derivatives and optimization algorithms for initial margins. His research interests lie in Mathematical  & Computational Physics,  Finance,  Monte-Carlo Methods and Non-linear Programming.