Kuien Liu

Yuan Wang, Borui Liao, Huijuan Huang et al.

Recent advances in video reward models and post-training strategies have improved text-to-video (T2V) generation. While these models typically assess visual quality, motion quality, and text alignment, they often overlook key structural distortions, such as abnormal object appearances and interactions, which can degrade the overall quality of the generative video. To address this gap, we introduce REACT, a frame-level reward model designed specifically for structural distortions evaluation in generative videos. REACT assigns point-wise scores and attribution labels by reasoning over video frames, focusing on recognizing distortions. To support this, we construct a large-scale human preference dataset, annotated based on our proposed taxonomy of structural distortions, and generate additional data using a efficient Chain-of-Thought (CoT) synthesis pipeline. REACT is trained with a two-stage framework: ((1) supervised fine-tuning with masked loss for domain knowledge injection, followed by (2) reinforcement learning with Group Relative Policy Optimization (GRPO) and pairwise rewards to enhance reasoning capability and align output scores with human preferences. During inference, a dynamic sampling mechanism is introduced to focus on frames most likely to exhibit distortion. We also present REACT-Bench, a benchmark for generative video distortion evaluation. Experimental results demonstrate that REACT complements existing reward models in assessing structutal distortion, achieving both accurate quantitative evaluations and interpretable attribution analysis.

Jiaquan Zhang, Fachrina Dewi Puspitasari, Songbo Zhang et al.

Neural operators offer an effective framework for learning solutions of partial differential equations for many physical systems in a resolution-invariant and data-driven manner. Existing neural operators, however, often suffer from instability in multi-layer iteration and long-horizon rollout, which stems from the unconstrained Euclidean latent space updates that violate the geometric and conservation laws. To address this challenge, we propose to constrain manifolds with low-rank Lie algebra parameterization that performs group action updates on the latent representation. Our method, termed Manifold Constraining based on Lie group (MCL), acts as an efficient \emph{plug-and-play} module that enforces geometric inductive bias to existing neural operators. Extensive experiments on various partial differential equations, such as 1-D Burgers and 2-D Navier-Stokes, over a wide range of parameters and steps demonstrate that our method effectively lowers the relative prediction error by 30-50\% at the cost of 2.26\% of parameter increase. The results show that our approach provides a scalable solution for improving long-term prediction fidelity by addressing the principled geometric constraints absent in the neural operator updates.

Zhenzhen Huang, Haoyu Bian, Jiaquan Zhang et al.

Several complex physical systems are governed by multi-scale partial differential equations (PDEs) that exhibit both smooth low-frequency components and localized high-frequency structures. Existing physics-informed neural network (PINN) methods typically train with fixed coordinate system inputs, where geometric misalignment with these structures induces gradient stiffness and ill-conditioning that hinder convergence. To address this issue, we introduce a mapping paradigm that reshapes the input coordinates through differentiable geometric compactification mappings and couples the geometric structure of PDEs with the spectral properties of residual operators. Based on this paradigm, we propose Geometric Compactification (GC)-PINN, a framework that introduces three mapping strategies for periodic boundaries, far-field scale expansion, and localized singular structures in the input domain without modifying the underlying PINN architecture. Extensive empirical evaluation demonstrates that this approach yields more uniform residual distributions and higher solution accuracy on representative 1D and 2D PDEs, while improving training stability and convergence speed.

Yitian Zhou, Chaoning Zhang, Zhenzhen Huang et al.

Non-stationary partial differential equations (PDEs) arise throughout scientific computing, where the dominant frequency content and energy distribution can drift over time. While efficient in PDE solving, many spectral neural operators apply a shared spectral response across rollout stages, leading to mismatch with time-varying spectra in non-stationary systems. To address this issue, we propose Time-Frequency Gated Spectral Neural Operator (TF-SNO), a state-adaptive framework with learnable time-frequency gating inside spectral blocks. TF-SNO extracts compact frequency-domain and physical-space statistics from the current state to generate modulation coefficients, enabling the spectral response to evolve with the dynamics. TF-SNO learns temporal variation implicitly from the evolving state without introducing an explicit time dimension or time embedding, keeping the modeling complexity low. We further embed the adaptive operator blocks to accurately capture the multi-scale features, thereby improving long-horizon stability. Experiments on six non-stationary PDE benchmarks in 1D and 2D demonstrate that TF-SNO significantly reduces prediction errors and improves robustness compared to strong baselines, with particularly clear gains in long rollout, suggesting the effectiveness of state-dependent spectral adaptation in modeling non-stationary physical systems.