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

2025-05-19

AI Summary

High-dimensional optimal control problems arising from ambiguity aversion in climate-economy modeling are computationally intractable for conventional numerical methods due to exponential complexity. Method: We formulate a continuous-time endogenous growth model and systematically benchmark multiple neural network architectures for solving ambiguity-averse climate-economy partial differential equations. We propose a physics-informed neural network (PINN)-based framework integrating finite-difference validation, multi-path mitigation constraints, and an uncertainty-embedding mechanism. Contribution/Results: Our approach achieves over 100× speedup relative to standard solvers while maintaining high accuracy: errors in carbon intensity trajectories and policy response sensitivities remain below 3.2%. This significantly enhances the computational tractability of carbon neutrality pathways under deep uncertainty and strengthens quantitative support for climate policy design.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Sustainability and carbon-aware systems for Web, mobile, and WoT

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.

Problem

• Solving high-dimensional climate-economic optimal control under uncertainty
• Comparing neural networks for accuracy in climate policy modeling
• Enhancing computational efficiency for uncertainty-aware mitigation strategies

Innovation

• Neural networks solve high-dimensional climate-economic control problems
• Continuous-time model integrates multiple mitigation pathways efficiently
• Architecture selection enhances accuracy and computational efficiency