Optimization of GPU Memory Usage for Importance Sampling in JAX Integral Calculations

[Qazalbash]

I am conducting numerical integration using JAX and require guidance on memory optimization for Importance Sampling. Specifically, I am generating approximately 10^5 samples and utilizing their weights relative to the underlying distribution. However, these weight arrays consume substantial GPU memory, frequently resulting in memory exhaustion errors. Given that these weights remain constant throughout the computation, I am exploring potential memory management strategies. My primary inquiry is whether CUDA constant memory could be leveraged to efficiently store and access these arrays, thereby mitigating GPU memory constraints. I would appreciate any insights and recommendations on this matter.

I have used the following formalism,

$$\int_{x\in\Omega} p(x)f(x)dx \approx \frac{1}{N}\sum_{i=1,x_i\sim q}^{N}{\frac{p(x_i)}{q(x_i)}f(x_i)} \approx \frac{1}{N}\sum_{i=1,x_i\sim q}^{N}{w(x_i)f(x_i)}$$