CLIMASIM — Climate Simulation with Scientific Machine Learning

Rapid climate scenario exploration remains constrained by a fundamental tension: General Circulation Models and Earth System Models provide comprehensive representations of atmosphere-ocean-carbon interactions but impose computational demands prohibitive for iterative policy evaluation, while Energy Balance Models offer tractability at significant cost to predictive fidelity. Conventional machine learning approaches, though computationally efficient, exhibit excessive data dependence and lack the mechanistic transparency essential for regulatory compliance and evidence-based climate policy. This methodological gap motivates our development of a scientific machine learning framework that augments coupled climate-carbon dynamics through Universal Differential Equations (UDEs), achieving simultaneous forecasting accuracy and interpretability for rapid scenario assessment.

We formulate a three-state coupled dynamical system governing surface temperature anomaly, deep ocean temperature anomaly, and atmospheric CO₂ concentration, incorporating radiative forcing, ocean-atmosphere heat exchange, and temperature-dependent carbon uptake feedback mechanisms. Our investigation proceeds through systematic experimental evaluation. First, we assess Neural Ordinary Differential Equations (Neural ODEs) as black-box dynamical system learners across three random initializations under 1% observational noise. Neural ODEs exhibit substantial forecasting errors—12.45% for surface temperature, 64.08% for ocean temperature, and 5.17% for CO₂ concentration at t=50 years—with progressive error amplification throughout the forecast horizon, demonstrating fundamental limitations in capturing climate dynamics without physical constraints.

Subsequently, we construct a UDE architecture that preserves known energy balance and carbon cycle physics while replacing the temperature-dependent carbon uptake term (βTC) with a neural network component. This hybrid formulation achieves forecasting errors below 0.2% across all climate variables for three distinct initializations, representing order-of-magnitude improvement over Neural ODEs while requiring 57.5% fewer training iterations. Comprehensive robustness analysis across six noise levels (1–25%) demonstrates exceptional stability, with percentage errors remaining below 0.74% up to 20% observational noise, degrading catastrophically only at the 25% threshold.

To ensure mechanistic transparency—critical for climate policy applications—we employ Sparse Identification of Nonlinear Dynamics (SINDy) for symbolic regression on learned neural network outputs. SINDy successfully recovers the correct functional form β·T·C across all noise regimes up to 20%, achieving 100% functional form recovery rate with average relative error of 25.22% at 1% noise. Performance metrics degrade systematically with increasing noise: R² decreases from 0.9985 (1% noise) to 0.7812 (20% noise), with complete interpretability breakdown at 25% noise (R²=0.4028). This characterizes operational bounds for symbolic recovery under realistic measurement uncertainty.

Comparative benchmarking against statistical baselines—Vector Autoregression (VAR) and Autoregressive Integrated Moving Average (ARIMA)—confirms UDE superiority in data-scarce regimes with known physical constraints. While VAR and ARIMA exhibit computational parsimony (21 and 10 parameters respectively versus 8,577 for UDE), they incur prediction errors exceeding 19% for temperature variables, rendering them unsuitable for high-fidelity forecasting. The UDE framework uniquely achieves the accuracy-efficiency-interpretability tradeoff essential for climate scenario exploration, enabling policymakers to evaluate interventions through mechanistically transparent simulations satisfying quantitative risk assessment requirements.

Our results establish that physics-informed machine learning enables accurate climate trajectory prediction while symbolic regression maintains interpretability, yielding a computationally efficient framework for rapid exploration of emission scenarios, carbon taxation policies, and adaptation strategies with explicit uncertainty quantification.