MoFE: A Novel Mixture-of-Experts Framework with Fourier Neural Operators for Cryptocurrency Forecasting

Bowen Liu; Mingming Sun

cs.LGAug 18, 2026

MoFE: A Novel Mixture-of-Experts Framework with Fourier Neural Operators for Cryptocurrency Forecasting

Authors: Bowen Liu, Mingming Sun

Organizations: School of Art and Science University of Rochester Rochester, USA · AGI Lab Beijing Institute of Mathematical Sciences and Applications Beijing, China

Abstract

Forecasting cryptocurrency prices remains a formidable challenge due to inherent non-stationarity, abrupt regime shifts, and multi-scale stochastic dependencies. Conventional deep learning models often struggle to capture complex underlying dynamics, frequently resulting in persistent phase-lagged predictions. To address these limitations, we propose MoFE, a novel deep learning framework that integrates Fourier Neural Operators (FNOs) within a Mixture-of-Experts (MoE) architecture. Rooted in the theoretical framework of stochastic differential equations, MoFE conceptualizes cryptocurrency volatility as a superposition of multi-frequency components, which includes user network based fundamental growth, mining costs and halving mechanism caused seasonal volatility, and market sentiment-induced chaos. Specifically, specialized adaptive FNO (AFNO) and Convolution dual-domain experts learn continuous function-to-function mappings to encapsulate global spectral trends, cyclical adjustments and microstructures, while a dynamic gating based MoE mechanism enables adaptive strategy switching across diverse market regimes. Extensive experiments on Bitcoin datasets spanning January 2020 to December 2025 demonstrate that MoFE achieves state-of-the-art (SOTA) performance in both T+1 and T+5 forecasting horizons. Notably, the model effectively mitigates the phase-lag effect, delivering superior Directional Accuracy (DA) and Information Coefficient (IC). In high-fidelity simulated trading environments, these predictive gains transfer into significant excess returns and robust risk-adjusted performance, characterized by a high Sharpe ratio.

Figures & tables

Fig. 1: The overall architecture of the MoFE model. The input features are processed through parallel global (FNO) and local (Conv) paths within the experts, dynamically weighted by the gating network.

Category	Hyperparameter	Value
Data	Look-back Window ( $L$ )	32
	Forecast Horizon ( $T_{p}$ )	1, 5
Model	Hidden Dimension ( $d_{model}$ )	48
	Frequency Modes	8
	Number of Experts ( $K$ )	2
	FNO Blocks	1

TABLE I: Hyperparameter Configuration of MoFE

Model	Statistical Metrics			Strategy Metrics		Profitability Metrics
Model	RMSE/ $($ \downarrow$ )	MAE/ $($ \downarrow$ )	$R^{2}$ ( $\uparrow$ )	IC ( $\uparrow$ )	DA (%) ( $\uparrow$ )	Sharpe ( $\uparrow$ )	W/L Ratio ( $\uparrow$ )	ROI (x) ( $\uparrow$ )
LSTM [ 9 ]	1618.35	1134.32	0.9819	0.0611	54.52%	1.00	1.00	1.48
GRU [ 10 ]	1605.20	1130.03	0.9819	0.0725	53.01%	1.03	1.24	1.16
iTransformer [ 11 ]	1603.96	1130.63	0.9822	0.1225	51.51%	2.42	0.96	2.75
S-Mamba [ 20 ]	1662.95	1183.44	0.9809	0.0127	54.82%	1.40	0.96	1.86
CryptoMamba [ 12 ]	1613.97	1145.64	0.9820	0.1123	51.81%	2.93	1.17	3.13

TABLE II: Performance comparison of MoFE against baseline models for T+1 prediction. The best results are in bold .

Model	Statistical Metrics			Strategy Metrics		Profitability Metrics
Model	RMSE/ $($ \downarrow$ )	MAE/ $($ \downarrow$ )	$R^{2}$ ( $\uparrow$ )	IC ( $\uparrow$ )	DA (%) ( $\uparrow$ )	Sharpe ( $\uparrow$ )	W/L Ratio ( $\uparrow$ )	ROI (x) ( $\uparrow$ )
LSTM [ 9 ]	3392.81	2596.66	0.9170	0.1015	56.10%	1.07	0.68	1.07
GRU [ 10 ]	3410.93	2618.38	0.9146	0.0326	52.44%	1.11	1.15	0.90
iTransformer [ 11 ]	3381.62	2592.32	0.9176	0.0760	53.66%	1.07	1.37	1.50
S-Mamba [ 20 ]	3443.05	2620.90	0.9146	0.0259	54.88%	0.82	1.05	0.92
CryptoMamba [ 12 ]	3650.63	2798.99	0.9040	0.0473	54.88%	0.96	1.17	1.60

TABLE III: Performance comparison of MoFE against baseline models for T+5 prediction. The best results are in bold .

Fig. 2: Visualized results of the comparison of predicted prices and real prices.

Fig. 3: Visualized results of the log returns prediction versus the real situations.

Fig. 4: Visualized results of the correlation scatter of the predicted log-returns and the realized market returns.

Model	Statistical Metrics			Strategy Metrics		Profitability Metrics
Model	RMSE/ $($ \downarrow$ )	MAE/ $($ \downarrow$ )	$R^{2}$ ( $\uparrow$ )	IC ( $\uparrow$ )	DA (%) ( $\uparrow$ )	Sharpe ( $\uparrow$ )	W/L Ratio ( $\uparrow$ )	ROI (x) ( $\uparrow$ )
1 Expert (w/o MoE)	1608.70	1127.54	0.9821	0.0903	51.51%	1.66	1.37	1.43
4 Experts (w MoE)	1658.03	1184.79	0.9810	0.0680	53.01%	1.29	1.16	1.70
2 Experts (w/o MoE)	1633.03	1142.99	0.9816	0.1077	54.52%	0.67	1.07	1.76
Conv. Kernel in Experts ( $n=1$ )	1597.61	1161.83	0.9824	0.1627	55.12%	2.11	1.13	2.52
Conv. Kernel in Experts ( $n=5$ )	1602.83	1129.21	0.9823	0.1324	54.22%	3.31	1.12	2.66

TABLE IV: Ablation Study

Fig. 5: Visualized results of two experts’ dynamic weights during mixing.

Fig. 6: Visualized results of the input vector contribution for the forecasting.

Fig. 7: Visualized results of four experts’ dynamic weights during mixing.

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Abstract

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