# Research outputs

#### (CDT Student names in bold)

**2024**

Coarse extrinsic curvature of Riemannian submanifolds

Authors: Marc Arnaudon, Xue-Mei Li,** Benedikt Petko**

Weak Convergence Analysis of Online Neural Actor-Critic Algorithms

Authors: **Samuel Chun-Hei Lam**, Justin Sirignano, **Ziheng Wang**

Deep Neural Network Initialization with Sparsity Inducing Activations

Authors: Ilan Price, **Nicholas Daultry Ball**, **Samuel C.H. Lam**, **Adam C. Jones**, Jared Tanner

Neural Networks-based Random Vortex Methods for Modelling Incompressible Flows

Authors: Vladislav **Cherepanov** and Sebastian W. Ertel

Random vortex dynamics and Monte-Carlo simulations for wall-bounded viscous flows

Authors: **Vladislav Cherepanov**, Sebastian W. Ertel, Zhongmin Qian and Jiang-Lun Wu

On the dynamics of the boundary vorticity for incompressible viscous flows

Authors: **Vladislav Cherepanov**, Jian-Guo Liu and Zhongmin Qian

Conditioned stochastic stability of equilibrium states on uniformly expanding repellers

Authors: **Bernat Bassols Cornudella**, **Matheus Manzatto de Castro **and** **Jeroen S. W. Lamb

Universality classes for percolation models with long-range correlations

** **Authors: **Christopher Chalhoub**, Alexander Drewitz, Alexis Prévost, Pierre-François Rodriguez

Constructive proofs for some semilinear PDEs on H²(e^{|x|²/4} , ℝ^d)

Authors: Maxime Breden (École Polytechnique, Paris) and **Hugo Chu**

Optimal Portfolio Choice with Cross-Impact Propagators

Authors: Eduardo Abi Jaber, Eyal Neuman and **Sturmius Tuschmann**

__Partially Stochastic Infinitely Deep Bayesian Neural Networks__

Authors: **Sergio Calvo-Ordonez, Matthieu Meunier, Francesco Piatti, Yuantao Shi**

**2023**

Noise-induced chaos: A conditioned random dynamics perspective

Authors: **Bernat Bassols-Cornudella** and Jeroen S. W. Lamb

VolGAN: a generative model for arbitrage-free implied volatility surfaces

** **Authors: **Milena Vuletić** and Rama Cont (working paper)

Learning Lie Group Symmetry Transformations with Neural Networks

Authors: Alex Gabel, **Victoria Klein**, Riccardo Valperga, Jeroen S. W. Lamb, Kevin Webster, Rick Quax and Efstratios Gavves

__Narratives from GPT-derived Networks of News, and a link to Financial Markets Dislocations__

Authors: **Deborah Miori** and Constantin Petrov

Kernel Limit of Recurrent Neural Networks Trained on Ergodic Data Sequences

Authors: **Samuel Chun-Hei Lam**, Justin Sirignano, Konstantinos Spiliopoulos

__Likelihood-based inference and forecasting for trawl processes: a stochastic optimization approach. __arXiv preprint arXiv:2308.16092 (2023) (with software: Ambit stochastics - a Github repository dedicated to the study of ambit fields and trawl processes https://github.com/danleonte/Ambit_Stochastics, doi:10.5281/zenodo.7081978.)

Authors: **Dan Leonte** and Almut ED Veraart

Binomial Cayley Graphs and Applications to Dynamics on Finite Spaces

Authors: **Bernat Bassols-Cornudella**, Francesco Viganò

Monte-Carlo method for incompressible fluid flows past obstacles

Authors: **Vladislav Cherepanov,** Zhongmin Qian

Author: **Matheus M. Castro, Giuseppe Tenaglia**

On the fluctuations of an SDE system modelling grid cells

Author: **Andrea Clini**

SHAPER: Can You Hear the Shape of a Jet?

Demba Ba, **Akshunna S. Dogra**, Rikab Gambhir, Abiy Tasissa, Jesse Thaler

Fluctuations of stochastic PDEs with long-range correlations

Author: **Luca Gerolla**, Martin Hairer, Xue-Mei Li

Calibration of Local Volatility Models with Stochastic Interest Rates using Optimal Transport

Gregoire Loeper, Jan Obloj, **Benjamin Joseph**

Smooth vs. Physical Solutions of the Navier-Stokes Equation

Authors: James Glimm, Jarret Petrillo, **Min Chul Lee**

DeFi: data-driven characterisation of Uniswap v3 ecosystem & an ideal crypto law for liquidity pools

Authors: **Deborah Miori**, Mihai Cucuringu

Execution and Statistical Arbitrage with Signals in Multiple Automated Market Makers

Authors: Álvaro Cartea, Fayçal Drissi, **Marcello Monga**

Coarse Ricci curvature of weighted Riemannian manifolds

Authors: Marc Arnaudon, Xue-Mei Li, **Benedikt Petko**

Singular SPDEs on Homogeneous Lie Groups

Authors: Avi Mayorcas, **Harprit Singh**

Strong convergence of parabolic rate 1 of discretisations of stochastic Allen-Cahn-type equations

Authors: Máté Gerencsér, **Harprit Singh**

Authors: Jeroen S.W. Lamb, **Giuseppe Tenaglia**, Dmitry Turaev

Looking forwards and backwards: dynamics and genealogies of locally regulated populations

Authors: Alison M. Etheridge, Thomas G. Kurtz, Ian Letter, Peter L. Ralph, **Terence Tsui Ho Lung**

Towards Evology: a Market Ecology Agent-Based Model of US Equity Mutual Funds II

Authors: **Aymeric Vie**, J. Doyne Farmer

Fin-GAN: Forecasting and Classifying Financial Time Series via Generative Adversarial Networks

Authors: **Milena Vuletić, Felix Prenzel, **Mihai Cucuringu

Dynamics of market making algorithms in dealer markets: Learning and tacit collusion

Authors: Rama Cont, **Wei Xiong**

Random neural networks for rough volatility

Authors: Antoine Jacquier, **Zan Zuric**

**2022**

Learning reversible symplectic dynamics

Authors: Riccardo Valperga, Kevin Webster, Dmitry Turaev, **Victoria Klein** and Jeroen S.W. Lamb

The Lyapunov spectrum for conditioned random dynamical systems

Authors: **Matheus M. Castro**, Dennis Chemnitz, **Hugo Chu**, Maximilian Engel, Jeroen S. W. Lamb, Martin Rasmussen

Authors: **Matheus M. Castro, Vincent P. H. Goverse, **Jeroen S. W. Lamb, Martin Rasmussen

The mean field limit of stochastic differential equation systems modelling grid cells

Authors: José A. Carrillo, **Andrea Clini**, Susanne Solem

Porous media equations with nonlinear gradient noise and Dirichlet boundary conditions

Authors: **Andrea Clini**

The entropy production of stationary diffusions

Authors: **Lancelot Da Costa**, Grigorios A. Pavliotis

Path integrals, particular kinds, and strange things

Authors: Karl Friston, **Lancelot Da Costa**, Dalton A. R. Sakthivadivel, Conor Heins, Grigorios A. Pavliotis, Maxwell Ramstead, Thomas Parr

Modelling non-reinforced preferences using selective attention

Authors: Noor Sajid, Panagiotis Tigas, Zafeirios Fountas, Qinghai Guo, Alexey Zakharov, **Lancelot Da Costa**

Authors: Conor Heins, **Lancelot Da Costa**

On Bayesian Mechanics: A Physics of and by Beliefs

Authors: Maxwell J D Ramstead, Dalton A R Sakthivadivel, Conor Heins, Magnus Koudahl, Beren Millidge, **Lancelot Da Costa**, Brennan Klein, Karl J Friston

The free energy principle made simpler but not too simple

Authors: Karl Friston, **Lancelot Da Costa**, Noor Sajid, Conor Heins, Kai Ueltzhöffer, Grigorios A. Pavliotis, Thomas Parr

Geometric Methods for Sampling, Optimisation, Inference and Adaptive Agents

Authors: Alessandro Barp, **Lancelot Da Costa, **Guilherme França, Karl Friston, Mark Girolami, Michael I. Jordan, Grigorios A. Pavliotis

A mixed generative model of auditory word repetition

Authors: Noor Sajid, Emma Holmes, **Lancelot Da Costa**, Cathy Price, Karl Friston

How Active Inference Could Help Revolutionise Robotics

Authors: **Lancelot Da Costa**, Pablo Lanillos, Noor Sajid, Karl Friston, Shujhat Khan

Universality of Winning Tickets: A Renormalization Group Perspective

Authors: William T. Redman, Tianlong Chen, Zhangyang Wang,** Akshunna S. Dogra**

Hamiltonian neural networks for solving equations of motion

Authors: Marios Mattheakis, David Sondak, **Akshunna S. Dogra**, Pavlos Protopapas

Authors: **Michael Giegrich**, Christoph Reisinger, Yufei Zhang

Learning reversible symplectic dynamics

Authors: Riccardo Valperga, Kevin Webster, **Victoria Klein**, Dmitry Turaev, Jeroen S. W. Lamb

Axioms for Quantum Gauge Fields

Authors: **Min Chul Lee**, James Glimm

Simulation methods and error analysis for trawl processes and ambit fields

Authors: **Dan Leonte**, Almut E. D. Veraart

On the fractal dimensions for deterministic and random substitution graph systems

Authors: **Ziyu Li**

The Short-Term Predictability of Returns in Order Book Markets: a Deep Learning Perspective

Authors: **Lorenzo Lucchese**, Mikko Pakkanen, Almut Veraart

Authors: Ben Hambly, **Julian Meier**, Andreas Sojmark

McKean-Vlasov Equations with Positive Feedback through Elastic Stopping Times

Authors: Ben Hambly, **Julian Meier**

Fast and Slow Optimal Trading with Exogenous Information

Authors: **Alessandro Micheli**, Eyal Neuman

SEC Form 13F-HR: Statistical investigation of trading imbalances and profitability analysis

Authors: **Deborah Miori**, Mihai Cucuringu

Returns-Driven Macro Regimes and Characteristic Lead-Lag Behaviour between Asset Classes

Authors: **Deborah Miori**, Mihai Cucuringu

Decentralised Finance and Automated Market Making: Execution and Speculation

Authors: Álvaro Cartea, Fayçal Drissi, **Marcello Monga**

Decentralised Finance and Automated Market Making: Permanent Loss and Optimal Liquidity Provision

Authors: Álvaro Cartea, Fayçal Drissi, **Marcello Monga**

Analysis and modeling of client order flow in limit order markets

Rama Cont, Mihai Cucuringu, Vacslav Glukhov, **Felix Prenzel**

Asymptotic Analysis of Deep Residual Networks

Authors: Rama Cont, **Alain Rossier**, Renyuan Xu

Convergence and Implicit Regularization Properties of Gradient Descent for Deep Residual Networks

Authors: Rama Cont, **Alain Rossier**, RenYuan Xu

Quantitative Universal Approximation Bounds for Deep Belief Networks

Authors: **Julian Sieber**, Johann Gehringer

On the (Non-)Stationary Density of Fractional-Driven Stochastic Differential Equations

Authors: Xue-Mei Li, Fabien Panloup, **Julian Sieber**

Markov decision processes with observation costs

Authors: Christoph Reisinger, **Jonathan Tam**

Topologies on unparameterised path space

Authors: Thomas Cass, **William F. Turner**

Towards Evology: a Market Ecology Agent-Based Model of US Equity Mutual Funds

Authors: **Aymeric Vie**, Maarten Scholl, Alissa M. Kleinnijenhuis, Doyne J. Farmer

Simulation of Arbitrage-Free Implied Volatility Surfaces

Authors: Rama Cont, **Milena Vuletic**

Authors: **Ziheng Wang**, Justin Sirignano

Authors: **Ziheng Wang**, Justin Sirignano

Interactions of market making algorithms: a study on perceived collusion

Authors: **Wei Xiong**, Rama Cont

Random vortex dynamics via functional stochastic differential equations

Authors: Zhongmin Qian, Endre Süli, **Yihuang Zhang**

Volatility forecasting with machine learning and intraday commonality

Authors: Chao Zhang, **Yihuang Zhang**, Mihai Cucuringu, Zhongmin Qian

Random vortex dynamics via functional stochastic differential equations

Authors: Zhongmin Qian, Endre Süli, **Yihuang Zhang**

**2021**

Authors: **Matheus M. Castro**, Jeroen S. W. Lamb, Guillermo Olicón Méndez, Martin Rasmussen

The mean field limit of stochastic differential equation systems modelling grid cells

Authors: José A. Carrillo, **Andrea Clini**, Susanne Solem

Authors: Thomas Parr, **Lancelot Da Costa**, Conor Heins, Maxwell James D. Ramstead, Karl J. Friston

Stochastic Chaos and Markov Blankets

Authors: Karl Friston, Conor Heins, Kai Ueltzhöffer, **Lancelot Da Costa**, Thomas Parr

A Drive towards Thermodynamic Efficiency for Dissipative Structures in Chemical Reaction Networks

Authors: Kai Ueltzhöffer, **Lancelot Da Costa**, Daniela Cialfi, Karl Friston

Active inference, Bayesian optimal design, and expected utility

Authors: Noor Sajid,** Lancelot Da Costa**, Thomas Parr, Karl Friston

Branching Time Active Inference: the theory and its generality

Authors: Théophile Champion, **Lancelot Da Costa**, Howard Bowman, Marek Grześ

Bayesian brains and the Rényi divergence

Authors: Noor Sajid, Francesco Faccio, **Lancelot Da Costa**, Thomas Parr, Jürgen Schmidhuber, Karl Friston

Bayesian Mechanics for Stationary Processes

Authors: **Lancelot Da Costa**, Karl Friston, Conor Heins, Grigorios A. Pavliotis

Signature asymptotics, empirical processes, and optimal transport

Authors: Thomas Cass, **Remy Messadene**

The dynamics of the Koopman-van Hove angular and linear momentum operators

Authors: **Remy Messadene**

Closed-Loop Nash Competition for Liquidity

Authors: **Alessandro Micheli**, Johannes Muhle-Karbe, Eyal Neuman

Scaling Properties of Deep Residual Networks

Authors: Alain-Sam Cohen, Rama Cont, **Alain Rossier**, Renyuan Xu

Mild Stochastic Sewing Lemma, SPDE in Random Environment, and Fractional Averaging

Authors: Xue-Mei Li, **Julian Sieber**

Functional Limit Theorems for Volterra Processes and Applications to Homogenization

Authors: Johann Gehringer, Xue-Mei Li, **Julian Sieber**

Modelling SARS-CoV-2 coevolution with genetic algorithms

Authors: **Aymeric Vie**

Authors: **Aymeric Vie**

Population network structure impacts genetic algorithm optimisation performance

Authors: **Aymeric Vie**

Global Convergence of the ODE Limit for Online Actor-Critic Algorithms in Reinforcement Learning

Authors:** Ziheng Wang**, Justin Sirignano

Authors: Serte Donderwinkel, **Zheneng Xie**

Tracking the vortex motion by using Brownian fluid particles

Authors: Zhongmin Qian, Youchun Qiu, **Yihuang Zhang**

Large and moderate deviations for importance sampling in the Heston model

Authors: Marc Geha, Antoine Jacquier, **Zan Zuric**

Deep Hedging under Rough Volatility

Authors: Blanka Horvath, Josef Teichmann, **Zan Zuric**

**2020**

The relationship between dynamic programming and active inference: the discrete, finite-horizon case

Authors: **Lancelot Da Costa**, Noor Sajid, Thomas Parr, Karl Friston, Ryan Smith

Authors: Karl Friston,** Lancelot Da Costa**, Danijar Hafner, Casper Hesp, Thomas Parr

Some interesting observations on the free energy principle

Authors: Karl Friston, **Lancelot Da Costa**, Thomas Parr

Active inference on discrete state-spaces: a synthesis

Authors: **Lancelot Da Costa**, Thomas Parr, Noor Sajid, Sebastijan Veselic, Victorita Neacsu, Karl Friston

Evidence of Crowding on Russell 3000 Reconstitution Events

Authors: **Alessandro Micheli, **Eyal Neuman

Slow-Fast Systems with Fractional Environment and Dynamics

Authors: Xue-Mei Li, **Julian Sieber**

Formulae for the Derivative of the Poincaré Constant of Gibbs Measures

Authors: **Julian Sieber**

Qualities, challenges and future of genetic algorithms: a literature review

Authors: **Aymeric Vie, **Alissa M. Kleinnijenhuis, Doyne J. Farmer

Asymptotic strong Feller property and local weak irreducibility via generalized couplings

Authors: Oleg Butkovsky, **Fabrice Wunderlich**

Robust pricing and hedging via neural SDEs

Authors: Patryk Gierjatowicz, Marc Sabate-Vidales, David Šiška, Lukasz Szpruch, **Žan Žurič**