Spherical Physics-informed Neural Operator with Multi-scale Coupling for Meteorological Downscaling

Yiqiang Ye; Yichi Wang; Haodi Zhang; Jiawei Wen; Jiahui Jiang; Zhaoyu Zhong; Jiangjian Yu; Chunxia Xiao

cs.AIOct 17, 2026

Spherical Physics-informed Neural Operator with Multi-scale Coupling for Meteorological Downscaling

Authors: Yiqiang Ye, Yichi Wang, Haodi Zhang, Jiawei Wen, Jiahui Jiang, Zhaoyu Zhong, Jiangjian Yu, Chunxia Xiao

Organizations: College of Computer and Software Engineering, Shenzhen University, Shenzhen, China · School of Computer Science, Wuhan University, Wuhan, China

Abstract

Meteorological downscaling is crucial for high-resolution regional climate forecasting and disaster early warning. While neural operators have emerged as a promising paradigm for modeling complex spatiotemporal mappings, existing frameworks often struggle with spherical manifold geometric distortions, inherent atmospheric multi-scale coupling mismatches, and lack of explicit atmospheric laws. We propose the Spherical Physics-informed Neural Operator, which utilizes a Spherical Laplacian Decomposition to partition atmospheric fields into hierarchical frequency components, maintaining exact point-wise correspondence across scales. To evaluate these representations at arbitrary locations, we introduce a localized spherical integral operator that approximates continuous kernel transforms via geometry-aware attention. Dynamical consistency is further enforced by embedding differentiable constraints into the learning process. Extensive experiments demonstrate that our framework attains superior accuracy and zero-shot generalization across various meteorological variables and unseen queries, representing a robust and interpretable solution for global-to-regional meteorological downscaling.

Figures & tables

Figure 1: Visualization of climate downscaling results at $2\times$ (training) and $4\times$ (OOD) factors. MSPNO generalizes across variables and scales while preserving spherical continuity and mitigating polar discontinuities.

Method	Multi-scale	Sphere	Physics
Class 1: Dot-product operators
DeepONet, LOCA	✗	✗	✗
Class 2: Fourier-based operator
FNO	✗	✗	✗
SFNO	✗	✓	✗
Class 3: Transformer-based operator

Table 1: Conceptual comparison of neural operator methods.

Figure 2: Overview. The Spherical Laplacian Encoder hierarchically decomposes multi-scale fluctuations on the spherical manifold. The Hybrid Location Encoding combines geodesic RBF kernels and Fourier features for continuous query evaluation. The Localized Spherical Integral Operator enables grid-agnostic evaluation through geometry-aware attention, while the Cross-scale Fusion module calibrates multi-frequency representations. Finally, differentiable Physics-Guided Constraints enforce dynamical consistency and physical fidelity.

Metric	Variable	Ours	OFormer	GNOT	LNO	DeepONet	IPOT	LOCA
MSE ( $\downarrow$ )	T2m	0.0045	0.0066	0.0117	0.0117	0.0127	0.0105	0.0102
	U10	0.1293	0.1397	0.1478	0.1478	0.2182	0.1471	0.1477
	V10	0.1637	0.1763	0.1870	0.1868	0.3871	0.1847	0.1865
	Z500	0.0009	0.0009	0.0010	0.0010	0.0034	0.0009	0.0010
	T850	0.0064	0.0074	0.0076	0.0076	0.0099	0.0075	0.0075
	R500	0.3526	0.3505	0.3511	0.3511	0.5380	0.3524	0.3512

Table 2: Quantitative comparison of different operator learning models in terms of MSE, RMSE, and ACC across multiple atmospheric variables. Best results are highlighted in bold , with second-best underlined.

Scales	MSE ( $\downarrow$ )	RMSE ( $\downarrow$ )	ACC ( $\uparrow$ )
1 (non-hierarchical)	0.1125	18.5787	0.8876
4 (Ours)	0.1117	18.4779	0.8881
8	0.1117	18.5175	0.8882

Table 3: Hyper-parameter study on the number of spatial scales in the spherical encoder. Results show that a 4-scale decomposition provides the optimal balance between accuracy and complexity.

Metric	Model	T2m	U10	V10	Z500	T850	R500	S850	Average
MSE ( $\downarrow$ )	Ours	0.0045	0.1293	0.1637	0.0009	0.0064	0.3526	0.1250	0.1117
	w/ Encoder (repl. Sphere)	0.0045	0.1298	0.1644	0.0009	0.0064	0.3540	0.1250	0.1121
	w/ Attn. Kernel (repl. Sphere)	0.0050	0.1323	0.1679	0.0009	0.0065	0.3511	0.1252	0.1127
	w/o Physics-Guided Objective	0.0046	0.1295	0.1642	0.0009	0.0064	0.3531	0.1249	0.1119
RMSE ( $\downarrow$ )	Ours	1.4322	1.9831	1.9225	102.8555	1.2558	19.8951	0.0015	18.4779
	w/ Encoder (repl. Sphere)	1.4308	1.9871	1.9261	103.3402	1.2575	19.9353	0.0015	18.5541

Table 4: Ablation study verifying spherical components and physics-guided objectives.

Figure 3: Zero-shot performance comparison across unseen query locations.

Method	Div. $\downarrow$	Vort. $\downarrow$	Vapor $\downarrow$	Total $\downarrow$
Ours	189.0197	78.5133	160.9526	428.4856
OFormer	202.2805	84.1339	171.9428	458.3572
GNOT	213.3368	88.0060	173.7128	475.0552
LNO	213.2525	87.9770	173.8381	475.0676
DeepONet	218.6825	89.9197	183.1225	491.7247
IPOT	211.7478	87.3884	173.8754	463.0116

Table 5: Physical consistency evaluation on

2\times

downscaling. We report mean absolute residuals (

\times 10^{-5}

) for divergence, vorticity, and vapor transport.

Figure 4: Visualization of scale-dependent spherical filters at multiple spatial scales.

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Accurate high-resolution wind field simulations are critical for resolving fine-scale atmospheric dynamics, yet the simulation of wind fields in Earth System Models (ESMs) remains limited by coarse spatial resolution and systematic biases. To address this, data-driven down scaling techniques have been widely used to enhance coarse-resolution ESM outputs. However, existing methods are typically tied to fixed discretizations, limiting generalization across models with different native resolutions. Here we formulate global near-surface wind downscaling as an operator-learning problem on continuous atmospheric state fields and develop a downscaling neural operator that maps coarse-scale fields to fine-scale counterparts across heterogeneous discretizations. The operator learning-based neural downscaling framework outperforms dominant baselines, recovers fine-scale physical structures, and generalizes to previously unseen ESMs and future climate scenarios without retraining, while preserving long-term wind projection trends. These findings establish a generalizable paradigm for high-resolution climate downscaling across diverse simulation outputs and future scenarios.

Abstract

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