Nanoporous materials (NPMs) are suitable for solving some of the society biggest challenges including carbon capture and conversion, storing hydrogen and methane, and sensing gases. The key challenge in discovering high-performing NPMs for a target application is that making and evaluating candidate NPMs requires performing resource-expensive wet-lab experiments. We consider the problem of discovering NPMs using existing experimental data of NPM evaluations. The overall goal is to find better NPMs than the best NPMs from the past experimental data. A simple approach is to create a surrogate model to match the objective values on the given dataset and employ it to score candidate NPMs to discover optimized NPMs. However, this surrogate model will fail because it does not have the appropriate search bias for the goal of optimization. To address this challenge, we propose a novel surrogate modeling approach that combines value matching loss with an optimization bias as regularizer. The key idea is to algorithmically realize search bias is to mimic the search behavior of monotonically increasing sequences of NPMs from the given dataset. Experiments on multiple real-world NPM discovery tasks demonstrate that our proposed surrogate model discovers significantly better NPMs than baselines including value matching surrogate model and one-step Bayesian optimization.