成果一.
我院马志明研究员与其合作者的论文Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic Representation被IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE接收发表。
摘要：In scenarios with limited available data, training the function-to-function neural PDE solver in an unsupervised manner is essential. However, the efficiency and accuracy of existing methods are constrained by the properties of numerical algorithms, such as finite difference and pseudo-spectral methods, integrated during the training stage. These methods necessitate careful spatiotemporal discretization to achieve reasonable accuracy, leading to significant computational challenges and inaccurate simulations, particularly in cases with substantial spatiotemporal variations. To address these limitations, we propose the Monte Carlo Neural PDE Solver (MCNP Solver) for training unsupervised neural solvers via the PDEs' probabilistic representation, which regards macroscopic phenomena as ensembles of random particles. Compared to other unsupervised methods, MCNP Solver naturally inherits the advantages of the Monte Carlo method, which is robust against spatiotemporal variations and can tolerate coarse step size. In simulating the trajectories of particles, we employ Heun's method for the convection process and calculate the expectation via the probability density function of neighbouring grid points during the diffusion process. These techniques enhance accuracy and circumvent the computational issues associated with Monte Carlo sampling. Our numerical experiments on convection-diffusion, Allen-Cahn, and Navier-Stokes equations demonstrate significant improvements in accuracy and efficiency compared to other unsupervised baselines.
论文链接：http://dx.doi.org/10.1109/TPAMI.2025.3548673
成果二.
我院赵国焕副研究员与其合作者的论文SDEs with critical time dependent drifts: strong solutions被PROBABILITY THEORY AND RELATED FIELDS接收发表。
摘要：This paper is a continuation of (R & ouml;ckner and Zhao, Bernoulli 29(1), 821 757-784 (2023)). Based on a compactness criterion for random fields in Wiener-Sobolev spaces, in this paper, we prove the strong solvability of time-inhomogeneous stochastic differential equations with drift coefficients in critical Lebesgue spaces, which gives an affirmative answer to a longstanding open problem. As an application, we also prove a regularity criterion for solutions of a stochastic system proposed by Constantin and Iyer (Comm. Pure. Appl. Math. 61(3): 330-345, 2008), which is closely related to the Navier-Stokes equations.
论文链接：http://dx.doi.org/10.1007/s00440-025-01390-9
成果三.
我院骆顺龙研究员与其合作者的论文Quantifying magic resource for quantum channels via channel-state duality被PHYSICAL REVIEW A接收发表。
摘要：According to the celebrated Gottesman-Knill theorem, magic resource (nonstabilizerness) is necessary to drive universal quantum computation. Thus characterization and quantification of magic resource for quantum states and quantum channels are significant issues. In this work, we propose a method to construct quantifiers of magic resource for quantum channels from those for quantum states by employing the channel-state duality to convert quantum channels to the corresponding Choi states. We focus on a specific quantifier of magic resource based on characteristic functions (Fourier transforms) of quantum states. This quantifier is well defined for all dimensions and easy to calculate, as opposed to those defined via discrete Wigner functions. It satisfies some desirable properties and provides an upper bound to the mana (a kind of logarithmic negativity of discrete Wigner functions) of quantum channels. Using this quantity, we evaluate the amount of magic resource for some typical quantum channels and compare them with some existing quantifiers of generating-power of magic resource. For the dephasing channels in prime dimensional systems, our quantifier of magic resource essentially characterizes the average generating power of magic resource, while, for general channels, they are quite different and some challenging issues arise.
论文链接：http://dx.doi.org/10.1103/PhysRevA.111.052420
成果四.
我院骆顺龙研究员与其合作者的论文Temporal correlating power of quantum channels被PHYSICAL REVIEW A接收发表。
摘要：Correlations, as intrinsic and intriguing features of quantum systems, have profound implications and applications in quantum information theory. Although substantial progress has been made in understanding and applying spatial correlations (i.e., those across different spatial systems at the same instant of time), temporal correlations (which emerge from the dynamics of a single quantum system across different instants of time) have been relatively less investigated. In this work, we first provide an axiomatic approach to temporal correlations by postulating natural requirements for a reasonable monotone of temporal correlations generated by a quantum channel. Then we study the temporal correlating power of quantum channels in terms of the Jordan product of quantum channels and compare it with the recently introduced notion of state over time. We introduce an information-theoretic monotone of such a power by exploiting the Jordan negativity and reveal its basic properties such as convexity, monotonicity, and unitary invariance. We further illustrate the monotone through several important channels and explicitly evaluate the corresponding temporal correlating power.
论文链接：http://dx.doi.org/10.1103/ms8v-qnj8
成果五.
我院袁铮博士后与其合作者的论文Tame maximal weights, relative types and valuations被ADVANCES IN MATHEMATICS接收发表。
摘要：In this article, we obtain a class of tame maximal weights (Zhou weights). Using Tian functions (the function of jumping numbers with respect to the exponents of a holomorphic function or the multiples of a plurisubharmonic function) as a main tool, we establish an expression of relative types (Zhou numbers) to these tame maximal weights in integral form, which shows that the relative types satisfy tropical multiplicativity and tropical additivity. Thus, the relative types to Zhou weights are valuations (Zhou valuations) on the ring of germs of holomorphic functions. We use Tian functions and Zhou numbers to measure the singularities of plurisubharmonic functions, involving jumping numbers and multiplier ideal sheaves. Especially, the relative types to Zhou weights characterize the division relations of the ring of germs of holomorphic functions. Finally, we consider a global version of Zhou weights on domains in Cn, which is a generalization of the pluricomplex Green functions, and we obtain some properties of them, including continuity and some approximation results.
论文链接：http://dx.doi.org/10.1016/j.aim.2025.110364
成果六.
我院朱湘禅研究员与其合作者的论文Non-unique Ergodicity for Deterministic and Stochastic 3D Navier-Stokes and Euler Equations被ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS接收发表。
摘要：We establish the existence of infinitely many statistically stationary solutions, as well as ergodic statistically stationary solutions, to the three dimensional Navier-Stokes and Euler equations in both deterministic and stochastic settings, driven by additive noise. These solutions belong to the regularity class C(R; H (& vartheta;) )boolean AND C (& vartheta;) (R; L-2) for some & vartheta; > 0 and satisfy the equations in an analytically weak sense. The solutions to the Euler equations are obtained as vanishing viscosity limits of statistically stationary solutions to the Navier-Stokes equations. Furthermore, regardless of their construction, every statistically stationary solution to the Euler equations within this regularity class, which satisfies a suitable moment bound, is a limit in law of statistically stationary analytically weak solutions to Navier-Stokes equations with vanishing viscosities. Our results are based on a novel stochastic version of the convex integration method, which provides uniform moment bounds in the aforementioned function spaces.
论文链接：http://dx.doi.org/10.1007/s00205-025-02102-2
成果七.
我院夏建明研究员与其合作者的论文Cash-Subadditive Risk Measures Without Quasi-Convexity被MATHEMATICS OF OPERATIONS RESEARCH接收发表。
摘要：In the literature on risk measures, cash subadditivity was proposed to replace cash additivity, motivated by the presence of stochastic or ambiguous interest rates and defaultable contingent claims. Cash subadditivity has been traditionally studied together with quasi-convexity, in a way similar to cash additivity with convexity. In this paper, we study cash-subadditive risk measures without quasi-convexity. One of our major results is that a general cash-subadditive risk measure can be represented as the lower envelope of a family of quasi-convex and cash-subadditive risk measures. Representation results of cashsubadditive risk measures with some additional properties are also examined. The notion of quasi-star-shapedness, which is a natural analogue of star-shapedness, is introduced, and we obtain a corresponding representation result via the lower envelope of normalized, quasi-convex, and cash-subadditive risk measures.
论文链接：http://dx.doi.org/10.1287/moor.2022.0312
成果八.
我院王勇研究员与其合作者的论文Genome diversity and signatures of natural selection in mainland Southeast Asia被NATURE接收发表。
摘要：Mainland Southeast Asia (MSEA) has rich ethnic and cultural diversity with a population of nearly 300 million1,2. However, people from MSEA are underrepresented in the current human genomic databases. Here we present the SEA3K genome dataset (phase I), generated by deep short-read whole-genome sequencing of 3,023 individuals from 30 MSEA populations, and long-read whole-genome sequencing of 37 representative individuals. We identified 79.59 million small variants and 96,384 structural variants, among which 22.83 million small variants and 24,622 structural variants are unique to this dataset. We observed a high genetic heterogeneity across MSEA populations, reflected by the varied combinations of genetic components. We identified 44 genomic regions with strong signatures of Darwinian positive selection, covering 89 genes involved in varied physiological systems such as physical traits and immune response. Furthermore, we observed varied patterns of archaic Denisovan introgression in MSEA populations, supporting the proposal of at least two distinct instances of Denisovan admixture into modern humans in Asia3. We also detected genomic regions that suggest adaptive archaic introgressions in MSEA populations. The large number of novel genomic variants in MSEA populations highlight the necessity of studying regional populations that can help answer key questions related to prehistory, genetic adaptation and complex diseases.
论文链接：http://dx.doi.org/10.1038/s41586-025-08998-w
成果九.
我院王益研究员与其合作者的论文Time-Asymptotic Stability of Generic Riemann Solutions for Compressible Navier-Stokes-Fourier Equations被ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS接收发表。
摘要：We establish the time-asymptotic stability of generic Riemann solutions to the one-dimensional compressible Navier-Stokes-Fourier equations. The Riemann solution under consideration is a generic combination of a shock, a contact discontinuity, and a rarefaction wave. We prove that the perturbed solution of Navier-Stokes-Fourier converges, uniformly in space as time goes to infinity, to an ansatz composed of viscous shock with time-dependent shift, a viscous contact wave and an inviscid rarefaction wave. This is a first resolution of the time-asymptotic stability of three waves of different kinds associated with the generic Riemann solutions. Our approach relies on the method of a-contraction with shifts and relative entropy, specifically applied to both the shock wave and the contact wave. It enables the application of a global energy method for the generic combination of three waves.
论文链接：http://dx.doi.org/10.1007/s00205-025-02116-w
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