**Transolver: A Fast Transformer Solver for PDEs on General Geometries** **Abstract:** Transformers have been widely applied to solve partial differential equations (PDEs), but they struggle with complex geometries and large-scale meshes. To address this, Transolver introduces a new Physics-Attention mechanism that adaptively splits the discretized domain into learnable slices of flexible shapes, grouping mesh points with similar physical states into the same slice. This approach allows Transolver to effectively capture intricate physical correlations under complex geometries, achieving linear computational complexity. Transolver outperforms state-of-the-art methods by 22% on six standard benchmarks and excels in large-scale industrial simulations, including car and airfoil designs. **Introduction:** Solving PDEs is crucial in various fields, but traditional numerical methods are often inefficient and complex. Deep models, particularly Transformers, offer a promising alternative by learning to approximate PDE solutions from data. However, applying Transformers directly to large-scale meshes with complex geometries is challenging due to computational efficiency and correlation learning issues. Transolver addresses these challenges by focusing on learning intrinsic physical states behind discretized geometries, enabling efficient and accurate PDE solving. **Physics-Attention:** Transolver's key innovation is the Physics-Attention mechanism, which decomposes the discretized domain into learnable slices and encodes each slice into a physics-aware token. This allows the model to capture complex underlying interactions by applying attention to these tokens, rather than directly processing individual mesh points. The method is designed to handle intricate physical correlations and complex geometries, making it suitable for a wide range of applications. **Experiments:** Extensive experiments on six standard benchmarks and two industrial-level design tasks demonstrate Transolver's superior performance. It achieves consistent state-of-the-art results and outperforms other methods in handling complex geometries and multiphysics interactions. Transolver also shows good scalability and out-of-distribution generalization, making it a robust and efficient solution for PDE-solving tasks.**Transolver: A Fast Transformer Solver for PDEs on General Geometries** **Abstract:** Transformers have been widely applied to solve partial differential equations (PDEs), but they struggle with complex geometries and large-scale meshes. To address this, Transolver introduces a new Physics-Attention mechanism that adaptively splits the discretized domain into learnable slices of flexible shapes, grouping mesh points with similar physical states into the same slice. This approach allows Transolver to effectively capture intricate physical correlations under complex geometries, achieving linear computational complexity. Transolver outperforms state-of-the-art methods by 22% on six standard benchmarks and excels in large-scale industrial simulations, including car and airfoil designs. **Introduction:** Solving PDEs is crucial in various fields, but traditional numerical methods are often inefficient and complex. Deep models, particularly Transformers, offer a promising alternative by learning to approximate PDE solutions from data. However, applying Transformers directly to large-scale meshes with complex geometries is challenging due to computational efficiency and correlation learning issues. Transolver addresses these challenges by focusing on learning intrinsic physical states behind discretized geometries, enabling efficient and accurate PDE solving. **Physics-Attention:** Transolver's key innovation is the Physics-Attention mechanism, which decomposes the discretized domain into learnable slices and encodes each slice into a physics-aware token. This allows the model to capture complex underlying interactions by applying attention to these tokens, rather than directly processing individual mesh points. The method is designed to handle intricate physical correlations and complex geometries, making it suitable for a wide range of applications. **Experiments:** Extensive experiments on six standard benchmarks and two industrial-level design tasks demonstrate Transolver's superior performance. It achieves consistent state-of-the-art results and outperforms other methods in handling complex geometries and multiphysics interactions. Transolver also shows good scalability and out-of-distribution generalization, making it a robust and efficient solution for PDE-solving tasks.