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This paper proposes a real-size, single-shot, high-speed, and energy-efficient tensorized optical multimodal fusion network (TOMFuN) on an electro-photonic large-scale III–V-on-Si in-memory compute engine. The TOMFuN architecture leverages a memory-efficient and low-complexity self-attention for the embedding network for the text information and tensor-train and CANDECOMP/PARAFAC decompositions for compressing the model parameters in the large-scale fully connected layers. Compared to full-size counterparts, our proposed network maintains a compatible inference accuracy in multimodal sentiment analysis tasks while requiring 92.8× fewer model parameters and 51.3× fewer hardware resources. Furthermore, the impact of photonic device imperfections on the TOMFuN architecture is investigated. The simulation results show that noise-aware on-chip training exhibits superior robustness. Finally, chip performance analysis shows that our TOMFuN inference accelerator has 230.73 PetaOps computational speed, 6.51 TOPS/W power efficiency, and 2.7 µs latency with the input dimensions of 1024. 

Operator learning has become a powerful tool in machine learning for modeling complex physical systems governed by partial differential equations (PDEs). Although Deep Operator Networks (DeepONet) show promise, they require extensive data acquisition. Physics-informed DeepONets (PI-DeepONet) mitigate data scarcity but suffer from inefficient training processes. We introduce Separable Operator Networks (SepONet), a novel framework that significantly enhances the efficiency of physics-informed operator learning. SepONet uses independent trunk networks to learn basis functions separately for different coordinate axes, enabling faster and more memory-efficient training via forward-mode automatic differentiation. We provide a universal approximation theorem for SepONet proving the existence of a separable approximation to any nonlinear continuous operator. Then, we comprehensively benchmark its representational capacity and computational performance against PI-DeepONet. Our results demonstrate SepONet's superior performance across various nonlinear and inseparable PDEs, with SepONet's advantages increasing with problem complexity, dimension, and scale. For 1D time-dependent PDEs, SepONet achieves up to 112× faster training and 82× reduction in GPU memory usage compared to PI-DeepONet, while maintaining comparable accuracy. For the 2D time-dependent nonlinear diffusion equation, SepONet efficiently handles the complexity, achieving a 6.44\% mean relative $$\ell_{2}$$ test error, while PI-DeepONet fails due to memory constraints. This work paves the way for extreme-scale learning of continuous mappings between infinite-dimensional function spaces. 

Operator learning has become a powerful tool in machine learning for modeling complex physical systems governed by partial differential equations (PDEs). Although Deep Operator Networks (DeepONet) show promise, they require extensive data acquisition. Physics-informed DeepONets (PI-DeepONet) mitigate data scarcity but suffer from inefficient training processes. We introduce Separable Operator Networks (SepONet), a novel framework that significantly enhances the efficiency of physics-informed operator learning. SepONet uses independent trunk networks to learn basis functions separately for different coordinate axes, enabling faster and more memory-efficient training via forward-mode automatic differentiation. We provide a universal approximation theorem for SepONet proving the existence of a separable approximation to any nonlinear continuous operator. Then, we comprehensively benchmark its representational capacity and computational performance against PI-DeepONet. Our results demonstrate SepONet's superior performance across various nonlinear and inseparable PDEs, with SepONet's advantages increasing with problem complexity, dimension, and scale. For 1D time-dependent PDEs, SepONet achieves up to 112× faster training and 82× reduction in GPU memory usage compared to PI-DeepONet, while maintaining comparable accuracy. For the 2D time-dependent nonlinear diffusion equation, SepONet efficiently handles the complexity, achieving a 6.44\% mean relative $$\el_2$$ test error, while PI-DeepONet fails due to memory constraints. This work paves the way for extreme-scale learning of continuous mappings between infinite-dimensional function spaces.