We introduce the Sumudu Neural Operator (SNO), a neural operator rooted in the properties of the Sumudu Transform. We leverage the relationship between the polynomial expansions of transform pairs to decompose the input space as coefficients, which are then transformed into the Sumudu Space, where the neural operator is parameterized. We evaluate the operator in ODEs (Duffing Oscillator, Lorenz System, and Driven Pendulum) and PDEs (Euler-Bernoulli Beam, Burger's Equation, Diffusion, Diffusion-Reaction, and Brus-selator). SNO achieves superior performance to FNO on PDEs and demonstrates competitive accuracy with LNO on several PDE tasks, including the lowest error on the Euler-Bernoulli Beam and Diffusion Equation. Additionally, we apply zero-shot super-resolution to the PDE tasks to observe the model's capability of obtaining higher quality data from low-quality samples. These preliminary findings suggest promise for the Sumudu Transform as a neural operator design, particularly for certain classes of PDEs.

Most metaheuristic algorithms rely on a few searched solutions to guide later searches during the convergence process for a simple reason: the limited computing resource of a computer makes it impossible to retain all the searched solutions. This also reveals that each search of most metaheuristic algorithms is just like a ballpark guess. To help address this issue, we present a novel metaheuristic algorithm called space net optimization (SNO). It is equipped with a new mechanism called space net; thus, making it possible for a metaheuristic algorithm to use most information provided by all searched solutions to depict the landscape of the solution space. With the space net, a metaheuristic algorithm is kind of like having a ``vision'' on the solution space. Simulation results show that SNO outperforms all the other metaheuristic algorithms compared in this study for a set of well-known single objective bound constrained problems in most cases.

You don't need a brain to learn. Slime molds, for example, solve mazes and navigate obstacles--all without a single neuron. Information about their environment is somehow stored across their bodies. A new paper suggests that samarium nickelate oxide (SNO, for short), a synthetic crystal, can mimic learning. SNO's ability comes from its environmental sensitivity.