老司机直播

AI algorithm improves predictive models of complex dynamical systems

Developed by 老司机直播 researchers, the new approach could have applications ranging from predicting the performance of aircraft engines to forecasting climate change
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From left to right: Professor Prasanth Nair and PhD student Kevin Course are the authors of a new paper in Nature that introduces a new machine learning algorithm that addresses the challenge of imperfect knowledge about system dynamics (supplied images)

Researchers at the University of Toronto have made a significant step towards enabling reliable predictions of complex dynamical systems when there are many uncertainties in the available data or missing information.

In , Prasanth B. Nair, a professor at the 老司机直播 Institute of Aerospace Studies (UTIAS) in the Faculty of Applied Science & Engineering, and UTIAS PhD candidate Kevin Course introduced a new machine learning algorithm that surmounts the real-world challenge of imperfect knowledge about system dynamics. The computer-based mathematical modelling approach is used for problem solving and better decision making in complex systems, where many components interact with each other.  

The researchers say the work could have numerous applications ranging from predicting the performance of aircraft engines to forecasting changes in global climate or the spread of viruses.  

鈥淔or the first time, we are able to apply state estimation to problems where we don鈥檛 know the governing equations, or the governing equations have a lot of missing terms,鈥 says Course, who is the paper鈥檚 first author.   

鈥淚n contrast to standard techniques, which usually require a state estimate to infer the governing equations and vice-versa, our method learns the missing terms in the mathematical model and a state estimate simultaneously.鈥  

State estimation, also known as data assimilation, refers to the process of combining observational data with computer models to estimate the current state of a system. Traditionally, it requires strong assumptions about the type of uncertainties that exist in a mathematical model.   

鈥淔or example, let鈥檚 say you have constructed a computer model that predicts the weather and at the same time, you have access to real-time data from weather stations providing actual temperature readings,鈥 says Nair. 鈥淒ue to the model鈥檚 inherent limitations and simplifications 鈥 which is often unavoidable when dealing with complex real-world systems 鈥 the model predictions may not match the actual observed temperature you are seeing.  

鈥淪tate estimation combines the model鈥檚 prediction with the actual observations to provide a corrected or better-calibrated estimate of the current temperature. It effectively assimilates the data into the model to correct its state.鈥  

However, it has been previously difficult to estimate the underlying state of complex dynamical systems in situations where the governing equations are completely or partially unknown. The new algorithm provides a rigorous statistical framework to address this long-standing problem.  

鈥淭his problem is akin to deciphering the 鈥榣aws鈥 that a system obeys without having explicit knowledge about them,鈥 says Nair, whose research group is developing algorithms for mathematical modelling of systems and phenomena that are encountered in various areas of engineering and science.  

A byproduct of Course and Nair鈥檚 algorithm is that it also helps to characterize missing terms or even the entirety of the governing equations, which determine how the values of unknown variables change when one or more of the known variables change.   

The main innovation underpinning the work is a reparametrization trick for stochastic variational inference with Markov Gaussian processes that enables an approximate Bayesian approach to solve such problems. This new development allows researchers to deduce the equations that govern the dynamics of complex systems and arrive at a state estimate using indirect and 鈥渘oisy鈥 measurements.  

鈥淥ur approach is computationally attractive since it leverages stochastic 鈥 that is randomly determined 鈥 approximations that can be efficiently computed in parallel and, in addition, it does not rely on computationally expensive forward solvers in training,鈥 says Course.   

While Course and Nair approached their research from a theoretical viewpoint, they were able to demonstrate practical impact by applying their algorithm to problems ranging from modelling fluid flow to predicting the motion of black holes.   

鈥淥ur work is relevant to several branches of sciences, engineering and finance as researchers from these fields often interact with systems where first-principles models are difficult to construct or existing models are insufficient to explain system behaviour,鈥 says Nair.  

鈥淲e believe this work will open the door for practitioners in these fields to better intuit the systems they study,鈥 adds Course. 鈥淓ven in situations where high-fidelity mathematical models are available, this work can be used for probabilistic model calibration and to discover missing physics in existing models.   

鈥淲e have also been able to successfully use our approach to efficiently train neural stochastic differential equations, which is a type of machine learning model that has shown promising performance for time-series datasets.鈥    

While the paper primarily addresses challenges in state estimation and governing equation discovery, the researchers say it provides a general groundwork for robust data-driven techniques in computational science and engineering.  

鈥淎s an example, our research group is currently using this framework to construct probabilistic reduced-order models of complex systems. We hope to鈥痚xpedite decision-making processes integral to the optimal design,鈥痮peration and control鈥痮f鈥痳eal-world systems,鈥 says Nair.   

鈥淎dditionally,鈥痺e are also studying how鈥痶he inference methods stemming from our research鈥痬ay鈥痮ffer deeper statistical insights into stochastic differential equation-based generative models that are now widely used in many artificial intelligence applications.鈥  

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