Zijian Zhou

Junchao Chen, Jin Song, Zijian Zhou et al.

In this paper, we study data-driven localized wave solutions and parameter discovery in the massive Thirring (MT) model via the deep learning in the framework of physics-informed neural networks (PINNs) algorithm. Abundant data-driven solutions including soliton of bright/dark type, breather and rogue wave are simulated accurately and analyzed contrastively with relative and absolute errors. For higher-order localized wave solutions, we employ the extended PINNs (XPINNs) with domain decomposition to capture the complete pictures of dynamic behaviors such as soliton collisions, breather oscillations and rogue-wave superposition. In particular, we modify the interface line in domain decomposition of XPINNs into a small interface zone and introduce the pseudo initial, residual and gradient conditions as interface conditions linked adjacently with individual neural networks. Then this modified approach is applied successfully to various solutions ranging from bright-bright soliton, dark-dark soliton, dark-antidark soliton, general breather, Kuznetsov-Ma breather and second-order rogue wave. Experimental results show that this improved version of XPINNs reduce the complexity of computation with faster convergence rate and keep the quality of learned solutions with smoother stitching performance as well. For the inverse problems, the unknown coefficient parameters of linear and nonlinear terms in the MT model are identified accurately with and without noise by using the classical PINNs algorithm.

Zhiheng Liu, Weiming Ren, Haozhe Liu et al.

Unified multimodal models (UMMs) aim to jointly perform multimodal understanding and generation within a single framework. We present TUNA, a native UMM that builds a unified continuous visual representation by cascading a VAE encoder with a representation encoder. This unified representation space allows end-to-end processing of images and videos for both understanding and generation tasks. Compared to prior UMMs with decoupled representations, TUNA's unified visual space avoids representation format mismatches introduced by separate encoders, outperforming decoupled alternatives in both understanding and generation. Moreover, we observe that stronger pretrained representation encoders consistently yield better performance across all multimodal tasks, highlighting the importance of the representation encoder. Finally, in this unified setting, jointly training on both understanding and generation data allows the two tasks to benefit from each other rather than interfere. Our extensive experiments on multimodal understanding and generation benchmarks show that TUNA achieves state-of-the-art results in image and video understanding, image and video generation, and image editing, demonstrating the effectiveness and scalability of its unified representation design.

Zijian Zhou, Zhenya Yan

In this paper, we study the neural tangent kernel (NTK) for general partial differential equations (PDEs) based on physics-informed neural networks (PINNs). As we all know, the training of an artificial neural network can be converted to the evolution of NTK. We analyze the initialization of NTK and the convergence conditions of NTK during training for general PDEs. The theoretical results show that the homogeneity of differential operators plays a crucial role for the convergence of NTK. Moreover, based on the PINNs, we validate the convergence conditions of NTK using the initial value problems of the sine-Gordon equation and the initial-boundary value problem of the KdV equation.

Shikun Liu, Kam Woh Ng, Wonbong Jang et al.

We present Kaleido, a family of generative models designed for photorealistic, unified object- and scene-level neural rendering. Kaleido operates on the principle that 3D can be regarded as a specialised sub-domain of video, expressed purely as a sequence-to-sequence image synthesis task. Through a systemic study of scaling sequence-to-sequence generative neural rendering, we introduce key architectural innovations that enable our model to: i) perform generative view synthesis without explicit 3D representations; ii) generate any number of 6-DoF target views conditioned on any number of reference views via a masked autoregressive framework; and iii) seamlessly unify 3D and video modelling within a single decoder-only rectified flow transformer. Within this unified framework, Kaleido leverages large-scale video data for pre-training, which significantly improves spatial consistency and reduces reliance on scarce, camera-labelled 3D datasets -- all without any architectural modifications. Kaleido sets a new state-of-the-art on a range of view synthesis benchmarks. Its zero-shot performance substantially outperforms other generative methods in few-view settings, and, for the first time, matches the quality of per-scene optimisation methods in many-view settings.

Arun Verma, Zhaoxuan Wu, Zijian Zhou et al.

Large Language Models (LLMs) are large-scale pretrained models that have achieved remarkable success across diverse domains. These successes have been driven by unprecedented complexity and scale in both data and computations. However, due to the high costs of training such models, brute-force trial-and-error approaches to improve LLMs are not feasible. Inspired by the success of inverse problems in uncovering fundamental scientific laws, this position paper advocates that inverse problems can also efficiently uncover scaling laws that guide the building of LLMs to achieve the desirable performance with significantly better cost-effectiveness.

Pengcheng Xie, Zihao Zhou, Zijian Zhou

This paper introduce a novel metric of an objective function f, we say VC (value change) to measure the difficulty and approximation affection when conducting an neural network approximation task, and it numerically supports characterizing the local performance and behavior of neural network approximation. Neural networks often suffer from unpredictable local performance, which can hinder their reliability in critical applications. VC addresses this issue by providing a quantifiable measure of local value changes in network behavior, offering insights into the stability and performance for achieving the neural-network approximation. We investigate some fundamental theoretical properties of VC and identified two intriguing phenomena in neural network approximation: the VC-tendency and the minority-tendency. These trends respectively characterize how pointwise errors evolve in relation to the distribution of VC during the approximation process.In addition, we propose a novel metric based on VC, which measures the distance between two functions from the perspective of variation. Building upon this metric, we further propose a new preprocessing framework for neural network approximation. Numerical results including the real-world experiment and the PDE-related scientific problem support our discovery and pre-processing acceleration method.

Zijian Zhou, Zhenya Yan

The third-order nonlinear Schrodinger equation (alias the Hirota equation) is investigated via deep leaning neural networks, which describes the strongly dispersive ion-acoustic wave in plasma and the wave propagation of ultrashort light pulses in optical fibers, as well as broader-banded waves on deep water. In this paper, we use the physics-informed neural networks (PINNs) deep learning method to explore the data-driven solutions (e.g., soliton, breather, and rogue waves) of the Hirota equation when the two types of the unperturbated and unperturbated (a 2% noise) training data are considered. Moreover, we use the PINNs deep learning to study the data-driven discovery of parameters appearing in the Hirota equation with the aid of solitons.