Emerging Trends in Complex Systems Modeling

The field of complex systems modeling is witnessing a significant shift towards the development of innovative methods that can efficiently capture the intricacies of real-world phenomena. Researchers are increasingly focusing on the integration of machine learning techniques with traditional modeling approaches to create more accurate and robust models. One notable direction is the use of neural cellular automata, which have shown great promise in modeling self-organizing processes and stochastic dynamics. Another area of interest is the application of generative models, such as diffusion-based models, to simulate complex systems and phenomena. These models have been successfully used to generate realistic images and simulate turbulence in fluid dynamics. Furthermore, there is a growing interest in the development of novel numerical methods, such as the Magnus method, to solve stochastic delay-differential equations and other complex mathematical models. Noteworthy papers in this area include the proposal of a novel PDE-driven corruption process for generative image synthesis, which generalizes existing PDE-based approaches and demonstrates improved diversity and quality of generated images. Additionally, the introduction of a stochastic framework for growth modeling and self-organization using mixtures of neural cellular automata has shown great potential in capturing the stochasticity of real-world biological and physical systems. The development of a latent score-based generative AI framework for learning stochastic, non-local closure models and constitutive laws in nonlinear dynamical systems has also been highlighted as a promising approach for modeling complex multiscale dynamical systems.

Sources

Neural Cellular Automata for ARC-AGI

Beyond Blur: A Fluid Perspective on Generative Diffusion Models

Magnus Methods for Stochastic Delay-Differential Equations

Closed-Loop Molecular Communication with Local and Global Degradation: Modeling and ISI Analysis

Local Learning Rules for Out-of-Equilibrium Physical Generative Models

Deep random difference method for high dimensional quasilinear parabolic partial differential equations

Mixtures of Neural Cellular Automata: A Stochastic Framework for Growth Modelling and Self-Organization

Stochastic and Non-local Closure Modeling for Nonlinear Dynamical Systems via Latent Score-based Generative Models

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