Checklist

For all authors... (a) Do the main claims made in the abstract and introduction accurately reflect the paper's contributions and scope? If you ran experiments... (a) Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)? [Yes] (b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)? If you used crowdsourcing or conducted research with human subjects... (a) Did you include the full text of instructions given to participants and screenshots, if applicable? [N/A] (b) Did you describe any potential participant risks, with links to Institutional Review Board (IRB) approvals, if applicable? [N/A] (c) Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation? This appendix is organized as follows. In Appendix A we provide a summary of the computational aspects of SPDEs used for data simulation and model definition, emphasizing the important role of the Fourier Transform (A.1) for simulating noise realizations of Wiener processes (A.2) and building numerical solvers for SPDEs (A.3).