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Neural Cellular Automata (NCA) are a powerful combination of machine learning and mechanistic modelling. We train NCA to learn complex dynamics from time series of images and PDE trajectories. Our method is designed to identify underlying…
Cellular automata (CA) are discrete-time dynamical systems with local update rules on a lattice. Despite their elementary definition, CA support a wide spectrum of macroscopic phenomena central to statistical physics: equilibrium and…
Cellular Automata (CA) have long been foundational in simulating dynamical systems computationally. With recent innovations, this model class has been brought into the realm of deep learning by parameterizing the CA's update rule using an…
Neural Cellular Automata (NCA) represent a powerful framework for modeling biological self-organization, extending classical rule-based systems with trainable, differentiable (or evolvable) update rules that capture the adaptive…
Neural Cellular Automata (NCA) models are trainable variations of traditional Cellular Automata (CA). Emergent motion in the patterns created by NCA has been successfully applied to synthesize dynamic textures. However, the conditions…
The abundance of data affords researchers to pursue more powerful computational tools to learn the dynamics of complex system, such as neural networks, engineered systems and social networks. Traditional machine learning approaches capture…
Adaptive dynamical networks are network systems in which the structure co-evolves and interacts with the dynamical state of the nodes. We study an adaptive dynamical network in which the structure changes on a slower time scale relative to…
Recurrent Neural Networks (RNNs) have shown great success in modeling time-dependent patterns, but there is limited research on their learned representations of latent temporal features and the emergence of these representations during…
Cellular automata and their differentiable counterparts, Neural Cellular Automata (NCA), are highly expressive and capable of surprisingly complex behaviors. This paper explores how NCAs perform when applied to tasks requiring precise…
Neural Cellular Automata (NCAs) are bio-inspired dynamical systems in which identical cells iteratively apply a learned local update rule to self-organize into complex patterns, exhibiting regeneration, robustness, and spontaneous dynamics.…
Knowledge about the hidden factors that determine particular system dynamics is crucial for both explaining them and pursuing goal-directed interventions. Inferring these factors from time series data without supervision remains an open…
This work aims to improve generalization and interpretability of dynamical systems by recovering the underlying lower-dimensional latent states and their time evolutions. Previous work on disentangled representation learning within the…
Systems of interacting objects often evolve under the influence of field effects that govern their dynamics, yet previous works have abstracted away from such effects, and assume that systems evolve in a vacuum. In this work, we focus on…
We propose a probabilistic cellular automata model for the spread of innovations, rumors, news, etc. in a social system. The local rule used in the model is outertotalistic, and the range of interaction can vary. When the range R of the…
Data-driven discovery of emergent dynamics is gaining popularity, particularly in the context of reaction-diffusion systems. These systems are widely studied across various fields, including neuroscience, ecology, epidemiology, and several…
Layered Cellular Automata (LCA) extends the concept of traditional cellular automata (CA) to model complex systems and phenomena. In LCA, each cell's next state is determined by the interaction of two layers of computation, allowing for…
Social dynamics is concerned primarily with interactions among individuals and the resulting group behaviors, modeling the temporal evolution of social systems via the interactions of individuals within these systems. In particular, the…
Discrete dynamical systems can exhibit complex behaviour from the iterative application of straightforward local rules. A famous example are cellular automata whose global dynamics are notoriously challenging to analyze. To address this, we…
Neural Cellular Automata (NCA) is a class of Cellular Automata where the update rule is parameterized by a neural network that can be trained using gradient descent. In this paper, we focus on NCA models used for texture synthesis, where…
Particle dynamics and multi-agent systems provide accurate dynamical models for studying and forecasting the behavior of complex interacting systems. They often take the form of a high-dimensional system of differential equations…