Cross-Disciplinary Modelling of Intelligent Systems Using Advanced Numerical Methods and Adaptive Algorithmic Design

The scientific challenge of modeling non-disciplinary complexity concerns not only the intelligent systems of the present such as pandemic forecasting or financial predicting; the problem of complex models is universal. These systems are noted as high-dimensional, multi-scale and non-stationary behavior, which could not be modeled proceeding with conventional and siloed approaches. Thus, it demands an integrated system that will utilize the resources of various fields of mathematics to their advantage. The paper presents a transdisciplinary modelling system, which is a synergic reciprocal combination of sophisticated numerical techniques and adaptive algorithm-based design. We no longer see complex phenomena in the world as problems of physics, biology, or finance but as universal dynamical systems, to be solved. Our idea is based on the hybrid approach, where we use Physics-Informed Neural Networks (PINNs) to directly incorporate governing laws into learning systems, yet use an adaptive solver to estimate dynamic parameters. We demonstrate with multi-scenario validation that this general framework is far superior to monolithic models in accuracy, robustness, as well as predictive capability and exists in a wide range of applications, such as in epidemiology and in computational finance. It is a major advance in a direction towards consilience in computational science and offers a general roadmap towards the construction of next-generation intelligent systems that are physically consistent and data-sensitive.