arXiv subjects

Weihong Zhang

Publications and source records attributed to Weihong Zhang.

8 recordsLinked to original sources

arXiv2026

Prescribed-Basis Coefficient-to-Coefficient Neural Operator for Partial Differential Equations

Operator learning provides a data-driven approach to approximating solution operators of partial differential equations, but its effectiveness depends strongly on how input and output functions are represented. Point-value representations can make the trainable map mesh-dependent and high-dimensional; snapshot-based POD/PCA reductions require aligned data and basis construction, while learned representations introduce additional trainable encoders, decoders, or neural bases. We propose the Fixed-Basis Coefficient-to-Coefficient Network (FB-C2CNet), which learns PDE solution maps in fixed, data-independent approximation spaces using prescribed bases as function encoders and decoders. Input observations are encoded by regularized least-squares projection onto bases such as finite element, random-feature, or radial-basis-function bases. A neural network maps the resulting input coefficients to output coefficients, and the fixed decoder reconstructs the solution at arbitrary target locations. This separation of basis selection from network training avoids neural basis learning and snapshot-based basis extraction, reduces the dimension of the trainable map, and lowers training cost. With suitable prescribed bases, FB-C2CNet also accommodates scattered, non-aligned, and sample-dependent observations. We analyze the stability--bias trade-off of regularized coefficient encoding and the intrinsic projection error determined by the output space. Experiments on elliptic, nonlinear time-dependent, weak-solution, high-dimensional, and inverse Stokes boundary-recovery problems demonstrate competitive accuracy with reduced trainable dimension and training cost, including for high-resolution and irregularly sampled data.

math.NA↗

arXiv2025

Ovis2.5 Technical Report

We present Ovis2.5, a successor to Ovis2 designed for native-resolution visual perception and strong multimodal reasoning. Ovis2.5 integrates a native-resolution vision transformer that processes images at their native, variable resolutions, avoiding the degradation from fixed-resolution tiling and preserving both fine detail and global layout -- crucial for visually dense content like complex charts. To strengthen reasoning, we train the model to move beyond linear chain-of-thought and perform reflection -- including self-checking and revision. This advanced capability is exposed as an optional "thinking mode" at inference time, allowing users to trade latency for enhanced accuracy on difficult inputs. The model is trained via a comprehensive five-phase curriculum that progressively builds its skills. The process begins with foundational visual and multimodal pretraining, advances through large-scale instruction tuning, and culminates in alignment and reasoning enhancement using DPO and GRPO. To scale these upgrades efficiently, we employ multimodal data packing and hybrid parallelism, yielding a significant end-to-end speedup. We release two open-source models: Ovis2.5-9B and Ovis2.5-2B. The latter continues the "small model, big performance" philosophy of Ovis2, making it ideal for resource-constrained, on-device scenarios. On the OpenCompass multimodal leaderboard, Ovis2.5-9B averages 78.3, marking a substantial improvement over its predecessor, Ovis2-8B, and achieving state-of-the-art results among open-source MLLMs in the sub-40B parameter range; Ovis2.5-2B scores 73.9, establishing SOTA for its size. Beyond aggregate scores, Ovis2.5 achieves leading results on STEM benchmarks, exhibits strong capabilities on grounding and video tasks, and achieves open-source SOTA at its scale for complex chart analysis.

cs.CV↗

arXiv2022

Fiber bundle topology optimization for surface flows

This paper presents a topology optimization approach for the surface flows on variable design domains. Via this approach, the matching between the pattern of a surface flow and the 2-manifold used to define the pattern can be optimized, where the 2-manifold is implicitly defined on another fixed 2-manifold named as the base manifold. The fiber bundle topology optimization approach is developed based on the description of the topological structure of the surface flow by using the differential geometry concept of the fiber bundle. The material distribution method is used to achieve the evolution of the pattern of the surface flow. The evolution of the implicit 2-manifold is realized via a homeomorphous map. The design variable of the pattern of the surface flow and that of the implicit 2-manifold are regularized by two sequentially implemented surface-PDE filters. The two surface-PDE filters are coupled, because they are defined on the implicit 2-manifold and base manifold, respectively. The surface Navier-Stokes equations, defined on the implicit 2-manifold, are used to describe the surface flow. The fiber bundle topology optimization problem is analyzed using the continuous adjoint method implemented on the first-order Sobolev space. Several numerical examples have been provided to demonstrate this approach, where the combination of the viscous dissipation and pressure drop is used as the design objective.

math.OC↗

arXiv2022

Combined parameterization of material distribution and surface mesh for stiffener layout optimization of complex surfaces

Stiffener layout optimization of complex surfaces is fulfilled within the framework of topology optimization. A combined parameterization method is developed in two aspects. One is to parameterize the material distribution of the stiffener layout by means of B-spline. The other is to build the mapping relationship from the known 3D surface mesh of the thin-walled structure to its parametric domain by means of mesh parameterization. The influence of mesh parameterization upon the stiffener layout is discussed to reveal the matching issue of the combined parameterization. 3D complex surfaces represented by the triangular mesh can be dealt with even though analytical parametric equations are not available. Some numerical examples are solved to demonstrate the direct advantage and effectiveness of the proposed method.

cs.CE↗

arXiv2021

SuperDTI: Ultrafast diffusion tensor imaging and fiber tractography with deep learning

Purpose: To propose a deep learning-based reconstruction framework for ultrafast and robust diffusion tensor imaging and fiber tractography. Methods: We propose SuperDTI to learn the nonlinear relationship between diffusion-weighted images (DWIs) and the corresponding tensor-derived quantitative maps as well as the fiber tractography. Super DTI bypasses the tensor fitting procedure, which is well known to be highly susceptible to noise and motion in DWIs. The network is trained and tested using datasets from Human Connectome Project and patients with ischemic stroke. SuperDTI is compared against the state-of-the-art methods for diffusion map reconstruction and fiber tracking. Results: Using training and testing data both from the same protocol and scanner, SuperDTI is shown to generate fractional anisotropy and mean diffusivity maps, as well as fiber tractography, from as few as six raw DWIs. The method achieves a quantification error of less than 5% in all regions of interest in white matter and gray matter structures. We also demonstrate that the trained neural network is robust to noise and motion in the testing data, and the network trained using healthy volunteer data can be directly applied to stroke patient data without compromising the lesion detectability. Conclusion: This paper demonstrates the feasibility of superfast diffusion tensor imaging and fiber tractography using deep learning with as few as six DWIs directly, bypassing tensor fitting. Such a significant reduction in scan time may allow the inclusion of DTI into the clinical routine for many potential applications.

eess.IV↗

arXiv2020

Topology optimization of surface flows

This paper presents a topology optimization approach for surface flows, which can represent the viscous and incompressible fluidic motions at the solid/liquid and liquid/vapor interfaces. The fluidic motions on such material interfaces can be described by the surface Navier-Stokes equations defined on 2-manifolds or two-dimensional manifolds, where the elementary tangential calculus is implemented in terms of exterior differential operators expressed in a Cartesian system. Based on the topology optimization model for fluidic flows with porous medium filling the design domain, an artificial Darcy friction is added to the area force term of the surface Navier-Stokes equations and the physical area forces are penalized to eliminate their existence in the fluidic regions and to avoid the invalidity of the porous medium model. Topology optimization for steady and unsteady surface flows can be implemented by iteratively evolving the impermeability of the porous medium on the 2-manifolds, where the impermeability is interpolated by the material density derived from a design variable. The related partial differential equations are solved by using the surface finite element method. Numerical examples have been provided to demonstrate this topology optimization approach for surface flows, including the boundary velocity driven flows, area force driven flows and convection-diffusion flows.

physics.comp-ph↗

arXiv2013

Fast Value Iteration for Goal-Directed Markov Decision Processes

Planning problems where effects of actions are non-deterministic can be modeled as Markov decision processes. Planning problems are usually goal-directed. This paper proposes several techniques for exploiting the goal-directedness to accelerate value iteration, a standard algorithm for solving Markov decision processes. Empirical studies have shown that the techniques can bring about significant speedups.

cs.AI↗

arXiv2013

A Method for Speeding Up Value Iteration in Partially Observable Markov Decision Processes

We present a technique for speeding up the convergence of value iteration for partially observable Markov decisions processes (POMDPs). The underlying idea is similar to that behind modified policy iteration for fully observable Markov decision processes (MDPs). The technique can be easily incorporated into any existing POMDP value iteration algorithms. Experiments have been conducted on several test problems with one POMDP value iteration algorithm called incremental pruning. We find that the technique can make incremental pruning run several orders of magnitude faster.

cs.AI↗