Deep neural networks are starting to show their potential for solving partial differential equations (PDEs)inavarietyofproblemdomains,includingturbulentflow,heattransfer,elastodynamics,and many more [1, 2, 3, 4, 5]. Thanks to their smooth and analytically-differentiable nature, implicit neural representations with periodic activation functions are emerging as a particularly attractive and powerful option in this context [4].

We discover that the recurrent update of these modelsresembles amonoid,leading ustoreformulate existing models using anovel monoid-based framework that we callmemoroids.

Thispaperproposes animplicit model-based multi-agent reinforcement learning method based onvalue decomposition methods. Under this method, agents can interact with thelearned virtual environment and evaluate thecurrent state value according to imagined future states in the latent space, making agents have the foresight. Our approach can be applied toanymulti-agent value decomposition method.