Data-driven predictions of the Lorenz system

Dubois, Pierre; Gomez, Thomas; Planckaert, Laurent; Perret, Laurent

doi:10.1016/j.physd.2020.132495

Cited by 43 publications

(19 citation statements)

References 21 publications

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“…And it is indeed so, but quite often the predictions are not correct and this can significantly impact the performance of the trading strategy. However, it has been shown that some techniques exist which can predict even quasi-periodic time-series, which is quite remarkable, considering the fundamentally chaotic nature of such time-series [29,30]. Depending on the nature of the time-series, the prediction interval is generally one time-step and for each new time-point prediction, the ground truth is fed back to the network.…”

Section: Predictionmentioning

confidence: 99%

Deep Reinforcement Learning For Trading - A Critical Survey

Millea¹

2021

Preprint

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Deep reinforcement learning (DRL) has achieved significant results in many Machine Learning (ML) benchmarks. In this short survey we provide an overview of DRL applied to trading on financial markets, including a short meta-analysis using Google Scholar, with an emphasis on using hierarchy for dividing the problem space as well as using model-based RL to learn a world model of the trading environment which can be used for prediction. In addition, multiple risk measures are defined and discussed, which not only provide a way of quantifying the performance of various algorithms, but they can also act as (dense) reward-shaping mechanisms for the agent. We discuss in detail the various state representations used for financial markets, which we consider critical for the success and efficiency of such DRL agents. The market in focus for this survey is the cryptocurrency market.

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Section: Predictionmentioning

confidence: 99%

Deep Reinforcement Learning For Trading - A Critical Survey

Millea¹

2021

Preprint

View full text Add to dashboard Cite

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“…It is, indeed, so, but quite often the predictions are not correct, and this can significantly impact the performance of the trading strategy. However, it has been shown that some techniques exist which can predict even quasi-periodic timeseries, which is quite remarkable, considering the fundamentally chaotic nature of such time-series [29,30]. Depending on the nature of the time-series, the prediction interval is generally one time-step, and for each new time-point prediction, the ground truth is fed back to the network.…”

Section: Predictionmentioning

confidence: 99%

Deep Reinforcement Learning for Trading—A Critical Survey

Millea

2021

Data

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Deep reinforcement learning (DRL) has achieved significant results in many machine learning (ML) benchmarks. In this short survey, we provide an overview of DRL applied to trading on financial markets with the purpose of unravelling common structures used in the trading community using DRL, as well as discovering common issues and limitations of such approaches. We include also a short corpus summarization using Google Scholar. Moreover, we discuss how one can use hierarchy for dividing the problem space, as well as using model-based RL to learn a world model of the trading environment which can be used for prediction. In addition, multiple risk measures are defined and discussed, which not only provide a way of quantifying the performance of various algorithms, but they can also act as (dense) reward-shaping mechanisms for the agent. We discuss in detail the various state representations used for financial markets, which we consider critical for the success and efficiency of such DRL agents. The market in focus for this survey is the cryptocurrency market; the results of this survey are two-fold: firstly, to find the most promising directions for further research and secondly, to show how a lack of consistency in the community can significantly impede research and the development of DRL agents for trading.

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“…In addition, because it was possible that these two types would do better at replicating specific aspects of the overall solution, we also evaluated a superposition of the two. Time series surrogates often use recurrent NN (Zhang and Xiao, 2000 ; Dubois et al, 2020 ). Similarly, deep generative models have been shown to be useful to sample from high dimensional space, as in the case of molecular dynamics and chemical reaction modeling (Chen and Ferguson, 2018 ; Noé et al, 2019 , 2020 ; Zhang et al, 2019 ; Gkeka et al, 2020 ; Kasim et al, 2020 ).…”

Section: Introductionmentioning

confidence: 99%

Deep Learning Approaches to Surrogates for Solving the Diffusion Equation for Mechanistic Real-World Simulations

et al. 2021

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In many mechanistic medical, biological, physical, and engineered spatiotemporal dynamic models the numerical solution of partial differential equations (PDEs), especially for diffusion, fluid flow and mechanical relaxation, can make simulations impractically slow. Biological models of tissues and organs often require the simultaneous calculation of the spatial variation of concentration of dozens of diffusing chemical species. One clinical example where rapid calculation of a diffusing field is of use is the estimation of oxygen gradients in the retina, based on imaging of the retinal vasculature, to guide surgical interventions in diabetic retinopathy. Furthermore, the ability to predict blood perfusion and oxygenation may one day guide clinical interventions in diverse settings, i.e., from stent placement in treating heart disease to BOLD fMRI interpretation in evaluating cognitive function (Xie et al., 2019; Lee et al., 2020). Since the quasi-steady-state solutions required for fast-diffusing chemical species like oxygen are particularly computationally costly, we consider the use of a neural network to provide an approximate solution to the steady-state diffusion equation. Machine learning surrogates, neural networks trained to provide approximate solutions to such complicated numerical problems, can often provide speed-ups of several orders of magnitude compared to direct calculation. Surrogates of PDEs could enable use of larger and more detailed models than are possible with direct calculation and can make including such simulations in real-time or near-real time workflows practical. Creating a surrogate requires running the direct calculation tens of thousands of times to generate training data and then training the neural network, both of which are computationally expensive. Often the practical applications of such models require thousands to millions of replica simulations, for example for parameter identification and uncertainty quantification, each of which gains speed from surrogate use and rapidly recovers the up-front costs of surrogate generation. We use a Convolutional Neural Network to approximate the stationary solution to the diffusion equation in the case of two equal-diameter, circular, constant-value sources located at random positions in a two-dimensional square domain with absorbing boundary conditions. Such a configuration caricatures the chemical concentration field of a fast-diffusing species like oxygen in a tissue with two parallel blood vessels in a cross section perpendicular to the two blood vessels. To improve convergence during training, we apply a training approach that uses roll-back to reject stochastic changes to the network that increase the loss function. The trained neural network approximation is about 1000 times faster than the direct calculation for individual replicas. Because different applications will have different criteria for acceptable approximation accuracy, we discuss a variety of loss functions and accuracy estimators that can help select the best network for a particular application. We briefly discuss some of the issues we encountered with overfitting, mismapping of the field values and the geometrical conditions that lead to large absolute and relative errors in the approximate solution.

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Data-driven predictions of the Lorenz system

Cited by 43 publications

References 21 publications

Deep Reinforcement Learning For Trading - A Critical Survey

Deep Reinforcement Learning For Trading - A Critical Survey

Deep Reinforcement Learning for Trading—A Critical Survey

Deep Learning Approaches to Surrogates for Solving the Diffusion Equation for Mechanistic Real-World Simulations

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