Machine Learning for Dynamical Systems


Machine learning and dynamic systems can be combined to explore the intersection of their common mathematical features. In one direction, machine learning algorithms can be employed to infer nonlinear operators governing dynamical systems from data, with the goal of improving computational requirements for the simulation of very large and complex (sometimes, chaotic) systems. This could enable speedups in the orders of magnitude in simulation analysis (like uncertainty quantification), inverse modeling, and optimal control, at the cost of introducing errors within an accepted tolerance. Machine learning models of dynamical systems have the potential to transfer computational costs to low criticality moments with offline model training, and to introduce uncertainty aspects of the realistic case by means of data fusion. Once the model is trained, the hope is that the resulting model inference time be several orders of magnitude faster than that of the numerical solver.

Along this direction, it is important to characterize the type of optimization landscape that corresponds to learning from data governed by a dynamical system, such as a system of partial differential equations (PDEs), as this is likely to display different features than a classic machine-learning task like image recognition. These features and correlations need to be investigated and could be used to speed up the learning process, making it more explainable, and prevent the misconvergence problems that sometimes afflict neural networks. At IBM Research, we’re addressing this question and striving to characterize this landscape for a few relevant equations. The landscape topology and searchability near critical solutions is also a key objective, as building a surrogate model that can capture elusive solutions is particularly challenging.


Recently, we've been working on the design and development of physics-informed machine learning (PIML) algorithms and applications using the SimulAI toolkit. In it we've collected state-of-the-art methods to facilitate the use of these emerging techniques in a shared framework that aims to accelerate the construction of expensive solver surrogates. SimulAI also serves as a common testbed for our own internal research and experimentation, improving upon previous work, while also providing configurable pipelines which can be easily adapted to different purposes.


At IBM Research, we're combining the power of machine learning and dynamical systems theories to tackle the most challenging problems arising in climate risk and mitigation, from the simulation of large-scale water circulation in lakes, sea surface temperatures, to carbon dioxide concentration and dispersion in the atmosphere, and methane leaking identification, among others.