How to increase memory on the FPGA board?
The ram on the PYNQ-Z1 is a 256x16 module DDR3. They do make a 512x16 module in the same package. I haven't torn through the datasheet to see if they are directly compatible, but it looks close at first glance. If the chips are indeed compatible, you would need to find a BGA rework place to do the work of replacement. 



PYNQ-Z1 DDR3 Schematic 


It would be much easier to adjust your algorithm to use less memory, if you can store data (with slower access times) then store it on the SD card.

Another avenue would be to use a slower serial RAM with the GPIO pins. But also not recommended, as you would have to find a compatible RAM (Arduino shields may be compatible with the PYNQ just by glancing at it and they do have serial RAM shields) You would have to install the shield and write a hardware driver for it, then map it into your program memory.