Net-Zero: A Comparative Study on Neural Network Design for Climate-Economic PDEs Under Uncertainty

TL;DR

The paper tackles solving high-dimensional, uncertainty-robust climate-economic PDEs by benchmarking a range of neural network architectures against a finite-difference ground truth. It adopts a two-network adversarial framework where a value network $\mathcal{V}_\theta$ and a policy network $\mathcal{P}_\phi$ together approximate the Hamilton-Jacobi-Bellman equation derived from a continuous-time stochastic climate-economy with multiple mitigation pathways. Through rigorous FD-based ground truth on a $60^3$ grid, the study finds that simple MLP-based architectures often yield the best trade-off between accuracy and training efficiency, while certain advanced architectures (e.g., SIREN, self-attention) may underperform for this problem. The results provide practical guidance for scalable neural PDE solvers in climate policy analysis, highlighting that architecture choice—particularly for the value function—significantly affects performance, and suggesting that different architectures for value and policy can be advantageous. These insights enable more efficient and nuanced policy analyses under uncertainty and technology transitions.

Abstract

Climate-economic modeling under uncertainty presents significant computational challenges that may limit policymakers' ability to address climate change effectively. This paper explores neural network-based approaches for solving high-dimensional optimal control problems arising from models that incorporate ambiguity aversion in climate mitigation decisions. We develop a continuous-time endogenous-growth economic model that accounts for multiple mitigation pathways, including emission-free capital and carbon intensity reductions. Given the inherent complexity and high dimensionality of these models, traditional numerical methods become computationally intractable. We benchmark several neural network architectures against finite-difference generated solutions, evaluating their ability to capture the dynamic interactions between uncertainty, technology transitions, and optimal climate policy. Our findings demonstrate that appropriate neural architecture selection significantly impacts both solution accuracy and computational efficiency when modeling climate-economic systems under uncertainty. These methodological advances enable more sophisticated modeling of climate policy decisions, allowing for better representation of technology transitions and uncertainty-critical elements for developing effective mitigation strategies in the face of climate change.

Figures (3)

• Figure 1: Our neural PDE method for climate-economic models under uncertainty. Our approach builds on a climate-economic model, formulated as a Hamilton-Jacobi-Bellman equation. We compare various neural architectures within a two-network framework against finite-difference ground truth solutions.
• Figure 2: Performance comparison of different architecture combinations. On the left, we show the error with respect to our FD benchmark, in the middle, computational cost (1 is best, X means X times slower training times than the best case), and right is overall efficiency, combining error and computational cost. We highlight the best result in green, the worst in red. We also provide average results across rows and columns (avg).
• Figure 3: Comparison on the share of low-carbon capital (and 95%) confidence ranges), emulated by our model on different prices assumptions.