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  [itCppCon21].

Energy Identities for singular solutions to Geometric PDEs:

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

• On the soliton resolution conjecture for wave maps (2017) [Oxford PhD thesis]

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. We build a software suite  to perform Monte-Carlo simulations for 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]

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:

• Differentiable programming for Kohn-Sham DFT: energy derivatives with respect to the parameters of exchange-correlation functional at linear cost, with Evgeny Kadilenko  (2023) [ChemRxiv] [notebook]

We develop 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, with Gregory Dushkin (2023) [notebook]

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

Computational Geometry for Mirror Symmetry:

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

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

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

Machine Learning for tackling Climate Change:

• Importance Sampling Approach for Dynamic Stochastic Optimal Power Flow Control, with A. Lukashevich, A. Bulkin,  I. Makarov, Y. Maximov (2023) [arXiv]

• Accessing Convective Hazards Frequency Shift with Climate Change using Physics-Informed Machine Learning,  with Mikhail Mozikov, Ilya Makarov, Alexandr Bulkin, Daria Taniushkina, Yury Maximov (2023) [arXiv] [IEEE Access]

• Climate Change Impact on Agricultural Land Suitability: An Interpretable Machine Learning-Based Eurasia Case Study, with Valeriy Shevchenko, Daria Taniushkina, Aleksander Lukashevich, Aleksandr Bulkin, Kirill Kovalev, Veronika Narozhnaia, Nazar Sotiriadi, Alexander Krenke, Yury Maximov  (2023) [arXiv]

• Climate Change and Future Food Security: Predicting the Extent of Cropland Gain or Degradation, with Daria Tanushkina, Valeriy Shevchenko, Aleksander Lukashevich, Aleksandr Bulkin, Kirill Kovalev, Veronika Narozhnaia, Nazar Sotiriadi, Alexander Krenke, Yury  Maximov (2023) [arXiv]

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

  4. American Monte-Carlo with AAD

  5. Heston Model: Calibration and MC simulations

  6. Machine Learning applications

• 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] 

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 Geometry, PDEs, Computational Physics and Finance