Our Vision

We are a team of scientists and engineers working together to solve key challenges that the world is facing. We focus on using machine learning to optimize complex decision making and reduce inefficiencies.

What We Do

At present we are successfully deploying our machine learning techniques to optimize the electricity grid by improving advance planning of electricity production and distribution, resulting in decreased economic waste and environmental damage.

Our Impact

Reduced CO2 emissions and pollution.
Improved reliability of the grid.
Less waste and increased economic efficiency.


Research Areas

Energy Systems
Electricity cannot be economically stored at utility scales. Supply and demand must be balanced at all times, and the structure of the transmission grid massive amounts of inefficiency. In order to deal with these issues, and to ensure reliable access to power, the global standard is to centralize control under Independent System Operators, who coordinate the grid for electric utilities. The efficiency of the electricity grid is also of fundamental importance for achieving lower carbon emissions, and reducing the impact of coal pollution on human health. Understanding all aspects of the electrical grid and their properties and complexities is an area of our core focus at present.
Machine Learning
Invenia Lab’s machine learning is focused on systems with a fundamental importance to everyday life, but which are not dealt with efficiently. Our central interest is in optimizing complex decision-making and resource usage under uncertainty. In particular, the electricity grid offers data with unique properties, including many time series with complex structures, and operations that change rapidly. While our focus is on practical problems, we are also actively working on more fundamental research with a focus on AI, time series forecasting and decision-making.
Complex Systems
Complex Systems is a broad area of research focused on studying systems made of a large number of interacting components and the emergence of complex collective behaviors. Social systems, the brain, and electricity grids are examples. A related area of interest is Complex Adaptive Systems, referring to systems reorganizing themselves to solve complex problems. Neural Networks and Memristors are two such examples. We are focused on the practical aspects in the application of these tools, but also advancing the fields from a theoretical perspective.
Our interest in finance tools and techniques stems from our work in electricity grids, which provide unique challenges with transmission due to the physical properties of electricity. We are studying risk, the processes that improve the efficiency of the grid and the consequences of regulatory changes. There are also many interesting connections between finance, statistical mechanics and complex systems to explore.

Our Team / Researchers

We come from many backgrounds including machine learning, mathematics, physics, computer science, engineering and economics. We are all interested in problems that have a substantial impact on the world, specifically complex systems that involve economic and environmental efficiency.
Chief Executive Officer / Co-Founder
Matt Hudson
Matt co-founded Invenia, and has been CEO from the start. He started Invenia while at Microsoft, after majoring in political science and economics with additional studies in computer science and engineering. He has developed a deep knowledge of the electrical grid, complex networks, and machine learning.
Chief Technology Officer / Co-Founder
Christian Steinruecken
Christian completed his PhD under the supervision of Prof Sir David MacKay at the University of Cambridge (UK), and is a specialist in machine learning. He has led engineering projects in artificial intelligence, data compression and probabilistic programming. Christian believes that building intelligent technology is our best hope for making the world a better place.
Chief People Operations Officer / Co-Founder
Oksana Koval
Oksana is a co-founder of Invenia and is currently the Chief People Operations Officer, overseeing operations in Canada and the UK. She attended the University of Manitoba and Red River College, where she studied Business Administration, and Anthropology as a post-graduate. In her spare time, she also pursues research interests in Machine Learning and Archaeology.
Managing Director Invenia Labs/ Chief Science Officer / Co-Founder
Cozmin Ududec
Cozmin is a co-founder of Invenia, and is currently Managing Director of Invenia Labs in Cambridge and Chief Science Officer. He received his PhD in the foundations of quantum theory from the University of Waterloo, and is still puzzling over the quantum world in his spare time.
Scientific Advisor / Co-founder
David Duvenaud
David is a co-founder of Invenia, and assistant professor in computer science and statistics at the University of Toronto. He received his Ph.D. in machine learning from Cambridge University. He has also worked at Google Research, the Max Planck Institute for Intelligent Systems, and the Harvard Intelligent Probabilistic Systems group.
Alex Robson
Alex has a PhD in Biophysics from Oxford University, where he worked on applying machine learning techniques to model biological data. Since then he has worked on different applications of ML, one for a startup in the energy sector and most recently risk models in fintech. In his spare time, he can be found playing board games, and occasionally hacking around on personal ML projects.
Senior Researcher
Bella Wu
Bella got her PhD in engineering from the University of Cambridge, where she developed advanced signal processing techniques, including many based on Bayesian inference, for magnetic resonance applications. Before joining Invenia, Bella worked at a startup on building energy models that provide forecast and analysis for use in hedging, trading and investments. She is interested in combining mathematical modelling and machine learning with fundamental theories in fields such as engineering and economics to gain unique insights into complicated systems that have a significant social impact.
Senior Researcher
Chris Davis
Chris was formerly an Assistant Professor in Energy Informatics and Modelling at the University of Groningen. He received his PhD at Delft University of Technology, and his work covers topics related to Energy, Sustainability, Linked Data, Machine Learning, Data Visualization and Agent Based Modelling. Here are a few papers published by Chris: 1. Secondary Resources in the Bio-Based Economy: A Computer Assisted Survey of Value Pathways in Academic Literature 2. Electric vehicle charging in China’s power system: Energy, economic and environmental trade-offs and policy implications 3. The state of the states: Data-driven analysis of the US Clean Power Plan For the rest of Chris' published work, please refer to his Google Scholar profile.
Doyne Farmer
Doyne works with Invenia as a research advisor. Professor in the Mathematical Institute at the University of Oxford, and an External Professor at the Santa Fe Institute. His current research is in economics, including agent-based modeling, financial instability and technological progress. He was a founder of Prediction Company, a quantitative automated trading firm that was sold to the United Bank of Switzerland in 2006. His past research includes complex systems, dynamical systems theory, time series analysis and theoretical biology.
Eric Perim Martins
Eric received his PhD in Physics from the University of Campinas, where he worked on Nanotechnology problems using Computational Physical-Chemistry techniques. He then moved to Duke University where he worked on High-Throughput Materials Science methods before joining Invenia.
Research Advisor
Francesco Caravelli
Francesco's research focuses on statistical physics and complex systems, in particular complex networks, memristive circuits, econophysics and agent-based modelling. He is a theoretical physicist, interested in quantum and classical systems and the application of techniques of statistical physics and complexity to other disciplines such as economics, engineering and finance. He has been a Senior Researcher at Invenia Labs in Cambridge and a researcher at the London Institute for Mathematical Sciences, before moving as an Oppenheimer Fellow to Los Alamos National Laboratory.
Research Engineer
Glenn Moynihan
Glenn Moynihan is native of county Cork in Ireland but upped sticks to study Theoretical Physics at Trinity College Dublin where he received his Bachelors in 2013 and his PhD in 2018. His research focused on improving the accuracy and scope of linear-scaling density-functional theory applied to large-scale calculations of materials exhibiting strongly-correlated electrons.
Senior Researcher
James Requeima
James is a senior researcher at Invenia and a PhD student studying machine learning at the University of Cambridge in the Computational and Biological Learning Lab under the supervision of Dr. Richard Turner. His interests include Bayesian optimization, learning, approximate inference methods, and deep generative models. He previously completed a master’s in machine learning, speech and language technology at the University of Cambridge under the supervision of Dr. Zoubin Ghahramani and a master’s of mathematics from the McGill University under Daniel Wise. He is also a tenured member of the Department of Mathematics at Dawson College in Montréal
People Operations Manager
Joao Moraes
After completing a law degree Joao went into business through a variety of roles, ultimately completing an MBA at the University of Cambridge. His previous background includes managing all aspects of a restaurant chain, brand strategy consultancy, and leadership development.
Letif Mones
I received my PhD in computational chemistry from ELTE University, Hungary, where I was working on the methodological improvement of hybrid QM/MM approaches and free energy computations for complex systems. At University of Cambridge and later at University of Warwick I developed an efficient sampling technique in combination with Gaussian process regression, introduced a protocol for constructing high dimensional quantum surfaces of organic molecules using machine learning and developed universal preconditioners to enhance the performance of optimisation techniques.
Research Engineer
Lyndon White
Lyndon grew up in the small town of Busselton in Western Australia. Until recently he was
studying at the University of Western Australia in Perth. He has undergrad degrees in Pure
Mathematics and Computation and in Electrical and Electronic Engineering. His Ph.D. on
Natural Language Processing via Machine Learning (Titled "On the surprising capacity of linear
combinations of embeddings") is currently under examination. He has been programming Julia
since late 2014 (v0.3.0 days) and is currently a maintainer/contributor to some unreasonable
number of packages.
Mahdi Jamei
Mahdi Jamei received the B.Sc. degree in Science and Technology in 2013, M.Sc. in Electrical and Computer Engineering from Florida International University (FIU), Miami, FL in 2014 and Ph.D. in Electrical and Computer Engineering from Arizona State University (ASU), Tempe, AZ in 2018. His research interests lie primarily in developing computational analytic tools for power system employing mathematical and signal processing techniques. He has been studying the security challenges of interdependent critical infrastructures mainly power, cyber and gas networks over the past few years.
Research Engineer
Nick Robinson
Nick recently completed a masters in AI at Edinburgh University, having previously studied analytic philosophy at Cambridge. In between, he worked at ASI building machine learning models for all sorts of different companies.
Head of Architecture and Operations
Sascha McDonald
Sascha is a senior executive with a track record of developing and implementing strategies to drive revenues and service delivery within start-up and blue-chip businesses. He comes with extensive international experience, key expertise includes: designing enterprise architecture, delivering operational capability across people, processes and technology; leading business development activity and contract negotiations to generate £multi-million revenue streams; leading multiple teams within both matrix and direct management environments; and managing relationships at CxO level with clients, suppliers and strategic partners.
Wessel Bruinsma
Wessel is currently a PhD student at the University of Cambridge. He holds an MPhil in Machine Learning, Speech, and Language Technology also from the University of Cambridge. At Invenia, Wessel conducts research in the field of machine learning and investigates applications thereof. Research interests include probabilistic modelling, Bayesian nonparametrics, approximate inference, and signal processing.
Research Associate
Will Tebbutt
Will is currently a PhD student at the University of Cambridge, and occasionally advises on specific Machine Learning related matters at Invenia Labs. When not working he can be found playing the guitar, or listening to people play it well.
Zoubin Ghahramani
Zoubin works with Invenia as an advisor. He is also a professor of Information Engineering at the University of Cambridge, where he leads the Machine Learning Group consisting of about 30 researchers, and the Cambridge Liaison Director of the Alan Turing Institute, the UK's national institute for Data Science. His academic career includes concurrent appointments as one of the founding members of the Gatsby Computational Neuroscience Unit in London, and as a faculty member of CMU's Machine Learning Department for over 10 years. His current research interests include statistical machine learning, Bayesian non-parametrics, scalable inference, probabilistic programming, and building an automatic statistician. He has published over 250 papers, receiving over 30,000 citations (an h-index of 74).


Explore some of the papers published by people on the Invenia Labs team.
Memristive networks: From graph theory to statistical physics
This paper is an introduction to a very specific toy model of memristive networks, for which an exact differential equation for the internal memory which contains the Kirchhoff laws is known. In particular, we highlight how the circuit topology enters the dynamics via an analysis of directed graph. We try to highlight in particular the connection between the asymptotic states of memristors and the Ising model, and the relation to the dynamics and statics of disordered systems.
A. Zegarac and F. Caravelli
Business models design space for electricity storage systems: Case study of the Netherlands
Because of weather uncertainty and dynamics, power generation from some renewable energy technologies is variable. Electricity storage is recognized as a solution to better integrate variable renewable generation into the electricity system. Despite considerable growth in the research on the electricity storage, implementation of electricity storage systems (ESS) is globally negligible because of technical, institutional, and business model challenges. We use literature review and data analysis to provide a conceptual framework and a design space for ESS business models in the case of Dutch electricity sector by taking technological, institutional, and business model considerations into account. We provide a map of single-application business models for ESS in the Netherlands which can be used as a basis for making ESS application portfolios and evaluating ESS business models in other parts of the world as well. Furthermore, this research can be used to inform models that explore the evolution of ESS.
S.A.R. Mir Mohammadi Kooshknow, C.B. Davis
The Gaussian Process Autoregressive Regression Model (GPAR)
Multi-output regression models must exploit dependencies between outputs to maximise predictive performance. The application of Gaussian processes (GPs) to this setting typically yields models that are computationally demanding and have limited representational power. We present the Gaussian Process Autoregressive Regression (GPAR) model, a scalable multi-output GP model that is able to capture nonlinear, possibly input-varying, dependencies between outputs in a simple and tractable way: the product rule is used to decompose the joint distribution over the outputs into a set of conditionals, each of which is modelled by a standard GP. GPAR’s efficacy is demonstrated on a variety of synthetic and real-world problems, outperforming existing GP models and achieving state-of-the-art performance on the tasks with existing benchmarks.
Learning Causally-Generated Stationary Time Series
We present the Causal Gaussian Process Convolution Model (CGPCM), a doubly nonparametric model for causal, spectrally complex dynamical phenomena. The CGPCM is a generative model in which white noise is passed through a causal, nonparametric-window moving-average filter, a construction that we show to be equivalent to a Gaussian process with a nonparametric kernel that is biased towards causally-generated signals. We develop enhanced variational inference and learning schemes for the CGPCM and its previous acausal variant, the GPCM (Tobar et al., 2015b), that significantly improve statistical accuracy. These modelling and inferential contributions are demonstrated on a range of synthetic and real-world signals.
Wessel Bruinsma, Richard E. Turner
Correlations and Clustering in Wholesale Electricity Markets
We study the structure of locational marginal prices in day-ahead and real-time wholesale electricity markets. In particular, we consider the case of two North American markets and show that the price correlations contain information on the locational structure of the grid. We study various clustering methods and introduce a type of correlation function based on event synchronization for spiky time series, and another based on string correlations of location names provided by the markets. This allows us to reconstruct aspects of the locational structure of the grid.
Tianyu Cui, Francesco Caravelli, Cozmin Ududec
The mise en scène of memristive networks: effective memory, dynamics and learning
We discuss the properties of the dynamics of purely memristive circuits. In particular, we show that the amount of memory in a memristive circuit is constrained by the conservation laws of the circuit, and that the dynamics preserves the symmetry by means of a projection on this subspace. We obtain these results both for current and voltage controlled linear memristors. Moreover, we discuss the symmetries of the dynamics which are due to the circuit cohomology, and study the weak and strong non-linear regimes.
Francesco Caravelli
The complex dynamics of memristive circuits: analytical results and universal slow relaxation
Networks with memristive elements (resistors with memory) are being explored for a variety of applications ranging from unconventional computing to models of the brain. However, analytical results that highlight the role of the graph connectivity on the memory dynamics are still a few, thus limiting our understanding of these important dynamical systems. In this paper, we derive an exact matrix equation of motion that takes into account all the network constraints of a purely memristive circuit, and we employ it to derive analytical results regarding its relaxation properties. We are able to describe the memory evolution in terms of orthogonal projection operators onto the subspace of fundamental loop space of the underlying circuit. This orthogonal projection explicitly reveals the coupling between the spatial and temporal sectors of the memristive circuits and compactly describes the circuit topology. For the case of disordered graphs, we are able to explain the emergence of a power law relaxation as a superposition of exponential relaxation times with a broad range of scales using random matrices. This power law is also {\it universal}, namely independent of the topology of the underlying graph but dependent only on the density of loops. In the case of circuits subject to alternating voltage instead, we are able to obtain an approximate solution of the dynamics, which is tested against a specific network topology. These result suggest a much richer dynamics of memristive networks than previously considered.
Francesco Caravelli, Fabio Lorenzo Traversa, Massimiliano Di Ventra
Trajectories entropy in dynamical graphs with memory
In this paper we investigate the application of non-local graph entropy to evolving and dynamical graphs. The measure is based upon the notion of Markov diffusion on a graph, and relies on the entropy applied to trajectories originating at a specific node. In particular, we study the model of reinforcement-decay graph dynamics, which leads to scale free graphs. We find that the node entropy characterizes the structure of the network in the two parameter phase-space describing the dynamical evolution of the weighted graph. We then apply an adapted version of the entropy measure to purely memristive circuits. We provide evidence that meanwhile in the case of DC voltage the entropy based on the forward probability is enough to characterize the graph properties, in the case of AC voltage generators one needs to consider both forward and backward based transition probabilities. We provide also evidence that the entropy highlights the self-organizing properties of memristive circuits, which re-organizes itself to satisfy the symmetries of the underlying graph.
Francesco Caravelli
Conformity Driven Agents Support Ordered Phases in the Spatial Public Goods Game
We investigate the spatial Public Goods Game in the presence of conformity-driven agents on a bi-dimensional lattice with periodic boundary conditions. The present setting usually considers fitness-driven agents, i.e., agents that tend to imitate the strategy of their fittest neighbors. Here, fitness is a general property usually adopted to quantify the extent to which individuals are able to succeed, or at least to survive, in a competitive environment. However, when social systems are considered, the evolution of a population might be affected also by social behaviors as conformity, stubbornness, altruism, and selfishness. Although the term evolution can assume different meanings depending on the considered domain, here it corresponds to the set of processes that lead a system towards an equilibrium or a steady-state. In doing so, we use two types of strategy update rules: fitness-driven and conformity-driven. We map fitness to the agents' payoff so that richer agents are those most imitated by fitness-driven agents, while conformity-driven agents tend to imitate the strategy assumed by the majority of their neighbors. Numerical simulations aim to identify critical phenomena, on varying the amount of the relative density of conformity-driven agents in the population, and to study the nature of related equilibria. Remarkably, we find that conformity fosters ordered phases and may also lead to bistable behaviors.
Marco Alberto Javarone, Alberto Antonioni, Francesco Caravelli
Optimal growth trajectories with finite carrying capacity
We investigate the spatial Public Goods Game in the presence of conformity-driven agents on a bi-dimensional lattice with periodic boundary conditions. The present setting usually considers fitness-driven agents, i.e., agents that tend to imitate the strategy of their fittest neighbors. Here, fitness is a general property usually adopted to quantify the extent to which individuals are able to succeed, or at least to survive, in a competitive environment. However, when social systems are considered, the evolution of a population might be affected also by social behaviors as conformity, stubbornness, altruism, and selfishness. Although the term evolution can assume different meanings depending on the considered domain, here it corresponds to the set of processes that lead a system towards an equilibrium or a steady-state. In doing so, we use two types of strategy update rules: fitness-driven and conformity-driven. We map fitness to the agents' payoff so that richer agents are those most imitated by fitness-driven agents, while conformity-driven agents tend to imitate the strategy assumed by the majority of their neighbors. Numerical simulations aim to identify critical phenomena, on varying the amount of the relative density of conformity-driven agents in the population, and to study the nature of related equilibria. Remarkably, we find that conformity fosters ordered phases and may also lead to bistable behaviors.
Marco Alberto Javarone, Alberto Antonioni, Francesco Caravelli
Neurogenesis Paradoxically Decreases Both Pattern Separation and Memory Interference
The hippocampus has been the focus of memory research for decades. While the functional role of this structure is not fully understood, it is widely recognized as being vital for rapid yet accurate encoding and retrieval of associative memories. Since the discovery of adult hippocampal neurogenesis in the dentate gyrus by Altman and Das in the 1960's, many theories and models have been put forward to explain the functional role it plays in learning and memory. These models postulate different ways in which new neurons are introduced into the dentate gyrus and their functional importance for learning and memory. Few if any previous models have incorporated the unique properties of young adult-born dentate granule cells and the developmental trajectory. In this paper, we propose a novel computational model of the dentate gyrus that incorporates the developmental trajectory of the adult-born dentate granule cells, including changes in synaptic plasticity, connectivity, excitability and lateral inhibition, using a modified version of the Restricted Boltzmann machine. Our results show superior performance on memory reconstruction tasks for both recent and distally learned items, when the unique characteristics of young dentate granule cells are taken into account. Even though the hyperexcitability of the young neurons generates more overlapping neural codes, reducing pattern separation, the unique properties of the young neurons nonetheless contribute to reducing retroactive and proactive interference, at both short and long time scales. The sparse connectivity is particularly important for generating distinct memory traces for highly overlapping patterns that are learned within the same context.
Becker, Finnegan
Correlation Structure of Spiky Financial Data: The Case of Congestion in Day-Ahead Energy Markets
I study the correlation structure and argue that these should be ltered. I propose the use of di erent correlation measures other than Pearson, in particular a modi cation of Event Synchronization adapted to negative values or a ltered correlation matrix.
On Moments of the Integrated Exponential Brownian Motion
We present new exact expressions for a class of moments for the geometric Brownian motion, in terms of determinants, obtained using a recurrence relation and combinatorial arguments for the case of a Ito’s Wiener process. We then apply the obtained exact formulas to computing averages of the solution of the logistic stochastic differential equation via a series expansion, and compare the results to the solution obtained via Monte Carlo.
Caravelli, Mansur, Severini, Sindoni
Bounds on Transient Instability For Complex Ecosystems
Stability is a desirable property of complex ecosystems. If a community of interacting species is at a stable equilibrium point then it is able to withstand small perturbations without any adverse effect. In ecology, the Jacobian matrix evalufated at an equilibrium point is known as the community matrix, which represents the population dynamics of interacting species. The system’s asymptotic short- and long-term behaviour can be determined from eigenvalues derived from the community matrix. Here we use results from the theory of pseudospectra to describe intermediate, transient dynamics. We show that the transition from stable to unstable dynamics includes a region of transient instability, where the effect of a small perturbation is amplified before ultimately decaying. The shift from stability to transient instability depends on the magnitude of a perturbation, and we show how to determine lower and upper bounds to the maximum amplitude of perturbations. Of five different types of community matrix, we find that amplification is least severe with predatorprey interactions. This analysis is relevant to other systems whose dynamics can be expressed in terms of the Jacobian matrix. Through understanding transient instability, we can learn under what conditions multiple perturbations—multiple external shocks—will irrecoverably break stability.
Caravelli, Staniczenko
Multi-scaling of wholesale electricity prices
We empirically analyze the most volatile component of the electricity price time series from two North-American wholesale electricity markets. We show that these time series exhibit fluctuations which are not described by a Brownian Motion, as they show multi-scaling, high Hurst exponents and sharp price movements. We use the generalized Hurst exponent (GHE, H(q)) to show that although these time-series have strong cyclical components, the fluctuations exhibit persistent behaviour, i.e., H(q)>0.5. We investigate the effectiveness of the GHE as a predictive tool in a simple linear forecasting model, and study the forecast error as a function of H(q), with q=1 and q=2. Our results suggest that the GHE can be used as prediction tool for these time series when the Hurst exponent is dynamically evaluated on rolling time windows of size ≈50−100 hours. These results are also compared to the case in which the cyclical components have been subtracted from the time series, showing the importance of cyclicality in the prediction power of the Hurst exponent.
Ashtari, Aste, Caravelli, Di Matteo, Requeima, Ududec
Scale-free networks as an epiphenomenon of memory
Many realistic networks are scale-free, with small characteristic path lengths, high clustering, and power law in their degree distribution. They can be obtained by dynamical networks in which a preferential attachment process takes place. However, this mechanism is nonlocal, in the sense that it requires knowledge of the whole graph in order for the graph to be updated. Instead, if preferential attachment and realistic networks occur in physical systems, these features need to emerge from a local model. In this paper, we propose a local model and show that a possible ingredient (which is often underrated) for obtaining scale-free networks with local rules is memory. Such a model can be realised in solid-state circuits, using non-linear passive elements with memory such as memristors, and thus can be tested experimentally.
Caravelli, Di Ventra, Hamma

Join Us

Being a part of the Invenia Labs team presents an opportunity to work with and learn from amazing people with expertise in machine learning, theoretical physics, mathematics, complex systems, and computer science while contributing to research that has a positive impact on our society and the environment.

We find great purpose in our ability to change the world for the better. It's what drives us to to work hard and continuously improve. If our vision resonates with you and you are interested in joining us, please visit our career page at www.joininvenia.com to apply.
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