Our goal is to write a general spectral code in one and two dimensions for cuda GPUs. The spectral code will be adaptive enough to be used for two kinds of problems: (1) wave turbulence (2) neural field model. I discuss the relevance of each one. Linear waves appear in many hydrodynamic problems in fluids and plasma. For example, ocean waves, Alfven waves, drift waves, etc. Under typical physical conditions the nonlinear effects in these problems are small but not zero. A small nonlinearity can give rise to wave turbulence in such problems. There are three key questions in the problems of wave turbulence: (1) what is the scaling of the energy spectrum ? (2) mixing and transport by turbulence ? (3) Non-Gaussian statistics or intermittency. In practice, numerically these are very difficult problems. They require simulations in three dimensions of nonlinear partial differential equations (PDEs) with very high resolution such that the scaling ranges are large enough to extract reliable scaling exponents. They also need to be run very long to be able to capture non-Gaussian statistics. Fortunately, there exists a model of wave turbulence than can be used in both one and two dimensions to study many of these problems : the Majda-McLaughlin-Tabak model (MMT) [1] . The MMT model is particularly interesting because earlier works have shown that it cannot be captured by weak wave turbulence theories (quasi-Gaussian closures). In the last 25 years this model has been studied numerically but never in very high resolution, recent works have used 4096 grid points [2] . Recent works have not been able to reach very high resolution because they have not yet explored GPU computing for this problem. I intend to study it in very high resolution and numerically settle conclusively the questions (1) to (3) above within this model. A GPU computing this the correct approach because even at very high resolution, by virtue of being one or two dimensions, the required memory would fit in one single GPU card and the parallel computing capabilities of a single GPU card can be exploited to its maximum potential. Neural networks are nonlinear systems driven by stochastic noise. Biological neural networks are often locally connected and can be described in PDEs called neural field models, e.g., Wilson-Kowan equations. Recently, there has been renewed interest in studying fudamental properties of such neural fields. Most simulations are done, so far, in small resolution. Typical neural field problems are studied in two dimensions. Hence there are also problems where a spectral code in a single GPU can make significant impact. I have experience developing spectral codes in CUDA in one and two dimensions for the Navier--Stokes equation and the MMT model (one dimension). Now I intend to initiate a project to writing a general purpose cuda GPU spectral code both the classes of problems. [1] Majda, A.J., McLaughlin, D.W. and Tabak, E., 1997. A one-dimensional model for dispersive wave turbulence. Journal of Nonlinear Science, 7(1), pp.9-44. [2] Simonis, A. and Pan, Y., 2024. Transition from weak turbulence to collapse turbulence regimes in the Majda-McLaughlin-Tabak model. Physical Review E, 110(2), p.024202.