Machine Learning With Data Assimilation and Uncertainty Quantification for Dynamical Systems:A Review

Data assimilation(DA)and uncertainty quantification(UQ)are extensively used in analysing and reducing error propagation in high-dimensional spatial-temporal dynamics.Typical applications span from computational fluid dynamics(CFD)to geoscience and climate systems.Recently,much effort has been given in combining DA,UQ and machine learning(ML)techniques.These research efforts seek to address some critical challenges in high-dimensional dynamical systems,including but not limited to dynamical system identification,reduced order surrogate modelling,error covariance specification and model error correction.A large number of developed techniques and methodologies exhibit a broad applicability across numerous domains,resulting in the necessity for a comprehensive guide.This paper provides the first overview of state-of-the-art researches in this interdisciplinary field,covering a wide range of applications.This review is aimed at ML scientists who attempt to apply DA and UQ techniques to improve the accuracy and the interpretability of their models,but also at DA and UQ experts who intend to integrate cutting-edge ML approaches to their systems.Therefore,this article has a special focus on how ML methods can overcome the existing limits of DA and UQ,and vice versa.Some exciting perspectives of this rapidly developing research field are also discussed.Index Terms-Data assimilation(DA),deep learning,machine learning(ML),reduced-order-modelling,uncertainty quantification(UQ).

Strength and failure characteristics of marble spheres subjected to paired point loads

Failure of irregular rock samples may provide implications in the rapid estimation of rock strength,which is imperative in rock engineering practice.In this work,analytical,experimental and numerical investigations were carried out to study the mechanical properties and failure characteristics of rock spheres under paired point loads.Analytical solutions indicted that with the increase in sample size(contact angle)and decrease in Poisson’s ratio,the uneven tensile stress in theta direction decreased.Then laboratory experiments were carried out to investigate the load characteristics and failure mode of spherical marble samples with different sizes subjected to a pair of diametral point loads.The discrete element method(DEM)was adopted to study the failure process of rock spheres.The effect of the sphere diameter on the point load contact angle was examined in terms of peak load,crushed zone distribution and energy dissipation.Experimental and numerical results showed that the samples primarily fail in tension,with crushed zones formed at both loading points.With increase in the sample size,the contact angle,crushed area and total work increase.As the specimen diameter increases from 30 mm to 50 mm,the peak load on the specimen increases from 3.6 kN to 8.8 kN,and the percentage of crushed zone(ratio of crushing zone to sample radius,d/r)increased from 0.191 to 0.262.The results of the study have implications for understanding the failure of irregular rock specimens under point loading conditions and their size effects.

Pressure relief and structure stability mechanism of hard roof for gob-side entry retaining

In order to explore the pressure relief and structure stability mechanism of lateral cantilever structure in the stope under the direct coverage of thick hard roof and its impact on the gob-side entry retaining, a lateral cantilever fractured structural mechanical model was established on the basis of clarification for the stress environment of gob-side entry retaining, and the equation of roof given deformation and the balance judgment for fracture block were obtained. The optimal cantilever length was proposed based on the comparison of roof structural characteristics and the stress, deformation law of surrounding rocks under six different cantilever lengths by numerical simulation method. Double stress peaks exist on the sides of gob-side entry retaining and the entry located in the low stress area. The pressure of gob-side entry retaining can be relieved by reducing the cantilever length. However, due to the impact of arch structure of rock beam, unduly short cantilever would result in insufficient pressure relief and unduly long cantilever would bring larger roof stress which results in intense deformation. Therefore, there is optimal cantilever length, which was 7-8 m in this project that enables to achieve the minimum deformation and the most stabilized rock structure of entry retaining. An engineering case of gob-side entry retaining with the direct coverage of 10 m thick hard limestone roof was put forward, and the measured data verified the reasonability of conclusion.

Hydro-mechanical interaction effects and channelling in threedimensional fracture networks undergoing growth and nucleation

The flow properties of geomechanically generated discrete fracture networks are examined in the context of channelling.Fracture networks are generated by growing fractures in tension,modelling the low permeability rock as a linear elastic material.Fractures are modelled as discrete surfaces which grow quasi-statically within a three-dimensional(3D)volume.Fractures may have their locations specified as a simulation input,or be generated as a function of damage,quantified using the local variation in equivalent strain.The properties of the grown networks are shown to be a product of in situ stress,relative orientation of initial flaws,and competitive process of fracture interaction and growth.Fractures grow preferentially in the direction perpendicular to the direction of maximum tension and may deviate from this path due to mechanical fracture interaction.Flow is significantly channelled through a subset of the fractures in the full domain,consistent with observations of other real and simulated fractures.As the fracture networks grow,small changes in the geometry of the fractures lead to large changes in the locations and scale of primary flow channels.The flow variability and formation of channels are examined for two growing networks,one with a fixed amount of fractures,and another with nucleating fractures.The interaction between fractures is shown to modify the local stress field,and in turn the aperture of the fractures.Pathways for single-phase flow are the results of hydro-mechanical effects in fracture networks during growth.These are the results of changes to the topology of the network as well as the result of mechanical self-organisation which occurs during interaction leading to growth and intersection.

The oceanic cycles of the transition metals and their isotopes

The stable isotope systems of the transition metals potentially provide constraints on the current and past operation of the biological pump,and on the state of ocean redox in Earth history.Here we focus on two exemplar metals,nickel(Ni)and zinc(Zn).The oceanic dissolved pool of both elements is isotopically heavier than the known inputs,implying an output with light isotope compositions.The modern oceanic cycle of both these elements is dominated by biological uptake into photosynthesised organic matter and output to sediment.It is increasingly clear,however,that such uptake is associated with only very minor isotope fractionation.We suggest that the isotopic balance is instead closed by the sequestration of light isotopes to sulphide in anoxic and organic-rich sediments,so that it is ocean chemistry that controls these isotope systems,and suggesting a different but equally interesting array of questions in Earth history that can be addressed with these systems.

Direct Evidence of Coal Swelling and Shrinkage with Injecting CO_(2) and N_(2) Using in-situ Synchrotron X-ray Microtomography

Deep coal seams are one of the world’s most widespread deposits for carbon dioxide(C02)disposal and are generally located near large point sources of CO_(2)emissions.The injection of CO_(2)into coal seams has great potential to sequester CO_(2)while simultaneously enhancing coalbed methane(CO_(2)-ECBM)recovery.Pilot tests of CO_(2)-ECBM have been conducted in coal seams worldwide with favorable early results.However,one of the main technical barriers in coal seams needs to be resolved:Injecting CO_(2)reduces coal permeability and well injectivity.Here,using in situ synchrotron X-ray microtomography,we provide the first observational evidence that injecting nitrogen(N_(2))can reverse much of this lost permeability by reopening fractures that have closed due to coal swelling induced by CO_(2)adsorption.Our findings support the notion that injecting minimally treated flue gas-a mixture of mainly N_(2) and CO_(2)-is an attractive alternative for ECBM recovery instead of pure CO_(2)injection in deep coal seams.Firstly,flue gas produced by power plants could be directly injected after particulate removal,thus avoiding high CO_(2)-separation costs.Secondly,the presence of N_(2)makes it possible to maintain a sufficiently high level of coal permeability.These results suggest that flue-gas ECBM for deep coal seams may provide a promising path toward net-zero emissions from coal mines.

Model-guided design of a high performance and durability Ni nanofiber/ceria matrix solid oxide fuel cell electrode

Mixed ionic electronic conductors(MIECs)have attracted increasing attention as anode materials for solid oxide fuel cells(SOFCs)and they hold great promise for lowering the operation temperature of SOFCs.However,there has been a lack of understanding of the performance-limiting factors and guidelines for rational design of composite metal-MIEC electrodes.Using a newly-developed approach based on 3 D-tomography and electrochemical impedance spectroscopy,here for the first time we quantify the contribution of the dual-phase boundary(DPB)relative to the three-phase boundary(TPB)reaction pathway on real MIEC electrodes.A new design strategy is developed for Ni/gadolinium doped ceria(CGO)electrodes(a typical MIEC electrode)based on the quantitative analyses and a novel Ni/CGO fiber-matrix structure is proposed and fabricated by combining electrospinning and tape-casting methods using commercial powders.With only 11.5 vol%nickel,the designer Ni/CGO fiber-matrix electrode shows 32%and 67%lower polarization resistance than a nano-Ni impregnated CGO scaffold electrode and conventional cermet electrode respectively.The results in this paper demonstrate quantitatively using real electrode structures that enhancing DPB and hydrogen kinetics are more efficient strategies to enhance electrode performance than simply increasing TPB.

ESR Signal Intensity and Crystallinity of Quartz from Three Major Asian Dust Sources: Implication for Tracing the Provenances of Eolian Dust

We measured Electron Spin Resonance(ESR) signal intensity and Crystallinity Index(CI) of fine-(<16 m) and coarse-grained(>16 m) quartz in surface samples collected from the Taklimakan desert in western China, the Badain Juran, Tengger and Mu Us deserts in northern China, and the Gobi desert in southern Mongolia. The aim was to test if these two parameters can be used as the accurate provenance tracers of Asian dust. Coarse-grained quartz displays spatial variability of the ESR signal intensity within each desert and of the CI within the Taklimakan and the Mongolian Gobi deserts. Coarse-grained quartz derived from the Mongolian Gobi and northern China deserts can be differentiated from the Taklimakan desert using the ESR signal intensity. By contrast, variability of ESR signal intensity and CI of fine-grained quartz particles is distinct within the Taklimakan and the Mongolian Gobi deserts, but less significant in three deserts of northern China. Spatially, fine-grained dust originating from three major Asian dust sources(i.e., the Gobi-sandy deserts in western China, northern China and southern Mongolia) can be differentiated using the combination of the ESR and CI signals. Our results suggest that combination of the ESR and CI results can discriminate the sources of fine-grained dust better than coarse-grained dust, providing an effective approach to trace the provenance of fine-grained dust depositions on the land and in the ocean.

天然气水合物稳定带内流体压裂计算的程序耦合方法

海洋天然气水合物稳定带气烟囱结构中存在被水合物充填的裂隙,表明在自然条件下沉积物中曾发生过流体压裂以及相关的流体流动和水合物形成。在水合物稳定带内实施人为的流体压裂工程,并联合其他方法(如降压或注热)进行水合物开采,有望提高开采效率。水合物稳定带内,无论是自然条件下发生的流体压裂过程,还是人为实施的流体压裂工程,都存在水合物反应和沉积物裂隙变形之间的耦合响应。当前,已有不少数值程序对水合物反应与沉积物弹塑性变形的耦合过程进行了定量研究,但尚没有数值程序能够计算水合物反应和离散裂隙变形之间的耦合过程。文章将TOUGH+Hydrate程序、IC-FERST和Solidity两者的耦合程序进行了进一步耦合,为水合物稳定带内的流体压裂计算提供了一种耦合计算方法,同时通过一个算例初步验证了该耦合计算方法的可行性。验证结果表明,该耦合计算方法经进一步改进后有望应用于定量研究水合物稳定带内的裂隙变形和水合物反应过程。

非结构网格空气质量模式对东亚强沙尘暴的初步模拟研究

基于中国科学院大气物理研究所自主研发的嵌套网格空气质量数值预报模式（NAQPMS）和英国帝国理工学院应用计算与建模小组（AMCG）研制的有限元流体模式（Fluidity）,构建了非结构网格沙尘传输模式（Fluidity-Dust）,并模拟再现了2010年3月19-22日东亚强沙尘暴整个暴发、演变的三维立体动态过程,从整体上对这次沙尘事件有了全新的直观认识和了解。通过利用FY-2D卫星沙尘反演资料及MODIS（Moderate Resolution Imaging Spectroradiometer）卫星反演的气溶胶光学厚度（AOD）资料,可对模拟结果进行整体上对比验证;同时,利用中国9个城市站点的PM10（空气动力学当量直径小于等于10μm的颗粒物,即可吸入颗粒物）地面观测资料以及日本多个站点的激光雷达资料,逐一对比分析了不同地区PM10的时空分布以及沙尘传输经过时的垂直分布情况;并与NAQPMS模式的沙尘模拟结果进行了模式间的对比分析。对比结果均表明：该模式具有较好的模拟能力,能很好地模拟再现整个沙尘暴过程,为今后进一步运用自适应变网格技术以实现对沙尘暴的高精度追踪模拟奠定了基础。不同模式比较是量化模拟不确定性的重要方法。以往沙尘输送模式比较研究表明：起沙量模拟的不确定性是沙尘暴数值模拟的最大不确定来源。本文通过两个具有相同起沙方案的模式对同一沙尘事件的模拟,发现不同的平流方案以及不同的沉降计算也会对沙尘过程模拟产生重要影响。

An efficient source wavefield reconstruction scheme using single boundary layer values for the spectral element method

In the adjoint-state method, the forward-propagated source wavefield and the backward-propagated receiver wavefield must be available simultaneously either for seismic imaging in migration or for gradient calculation in inversion. A feasible way to avoid the excessive storage demand is to reconstruct the source wavefield backward in time by storing the entire history of the wavefield in perfectly matched layers. In this paper, we make full use of the elementwise global property of the Laplace operator of the spectral element method (SEM) and propose an efficient source wavefield reconstruction method at the cost of storing the wavefield history only at single boundary layer nodes. Numerical experiments indicate that the accuracy of the proposed method is identical to that of the conventional method and is independent of the order of the Lagrange polynomials, the element type, and the temporal discretization method. In contrast, the memory-saving ratios of the conventional method versus our method is at least N when using either quadrilateral or hexahedron elements, respectively, where N is the order of the Lagrange polynomials used in the SEM. A higher memorysaving ratio is achieved with triangular elements versus quadrilaterals. The new method is applied to reverse time migration by considering the Marmousi model as a benchmark. Numerical results demonstrate that the method is able to provide the same result as the conventional method but with about 1/25 times lower storage demand. With the proposed wavefield reconstruction method, the storage demand is dramatically reduced;therefore, in-core memory storage is feasible even for large-scale three-dimensional adjoint inversion problems.

Flow in Porous Media in the Energy Transition

1.Historical context Flow in porous media is encountered in a wide variety of natural and engineered settings,including gas exchange in lungs and blood vessels,water extraction from underground aquifers,hydrocarbon production,and microfluidics in drug delivery and food manufacturing.Underground rock is a porous medium that holds water and hydrocarbons,and is a potential storage site for carbon dioxide(CO_(2))and hydrogen.Many manufactured devices also contain porous media to allow the transport of gases and water,including fuel cells,electrolyzers,and electrocatalysts for CO_(2) reduction.Their performance is limited by how rapidly two fluid phases can flow through a porous layer.

Uncovering the creep deformation mechanism of rock-forming minerals using nanoindentation

The creep phenomenon of rocks is quite complex and the creep mechanisms are far from being well understood.Although laboratory creep tests have been carried out to determine the creep deformation of various rocks,these tests are expensive and time-consuming.Nanoindentation creep tests,as an alternative method,can be performed to investigate the mechanical and viscoelastic properties of granite samples.In this study,the reduced Young’s modulus,hardness,fracture toughness,creep strain rate,stress exponent,activation volume and maximum creep displacement of common rock-forming minerals of granite were calculated from nanoindentation results.It was found that the hardness decreases with the increase of holding time and the initial decrease in hardness was swift,and then it decreased slowly.The stress exponent values obtained were in the range from 4.5 to 22.9,which indicates that dislocation climb is the creep deformation mechanism.In addition,fracture toughness of granite’s rock-forming minerals was calculated using energy-based method and homogenization method was adopted to upscale the micro-scale mechanical properties to macro-scale mechanical properties.Last but not least,both three-element Voigt model and Burgers model fit the nanoindentation creep curves well.This study is beneficial to the understanding of the long-term mechanical properties of rock samples from a microscale perspective,which is of great significance to the understanding of localized deformation processes of rocks.

Utilization of Energy Storage and Hydrogen in Power and Energy Systems:Viewpoints from Five Aspects

Decarbonizing power systems is crucial to mitigating climate change impacts and achieving carbon neutrality.Increasing renewable energy supply can reduce greenhouse gas emissions and accelerate the decarbonization process.However,renewable energy sources(RESs)such as wind and solar power are characterized by intermittency and often non-dispatchability,significantly challenging their high-level integration into power systems.Energy storage is acknowledged as a vital indispensable solution for mitigating the intermittency of renewables such as wind and solar power and boosting the penetrations of renewables.In the CSEE JPES Forum,five well-known experts were invited to give keynote speeches,and the participating experts and scholars had comprehensive exchanges and discussions on energy storage technologies.Specifically,the views on the design,control,performance,and applications of new energy storage technologies,such as the fuel cell vehicle,water electrolysis,and flow battery,in the coordination and operation of power and energy systems were analyzed.The experts also provided experience that could be used to develop energy storage for constructing and decarbonizing new power systems.

Numerical simulation of three-dimensional breaking waves and its interaction with a vertical circular cylinder

Wave breaking plays an important role in wave-structure interaction. A novel control volume finite element method with adaptive unstructured meshes is employed here to study 3-D breaking waves. The numerical framework consists of a ＂volume of fluid＂ type method for the interface capturing and adaptive unstructured meshes to improve computational efficiency. The numerical model is validated against experimental measurements of breaking wave over a sloping beach and is then used to study the breaking wave impact on a vertical circular cylinder on a slope. Detailed complex interfacial structures during wave impact, such as plunging jet formation and splash-up are captured in the simulation, demonstrating the capability of the present method.

Reservoir and lithofacies shale classification based on NMR logging

Shale gas reservoirs have fine-grained textures and high organic contents,leading to complex pore structures.Therefore,accurate well-log derived pore size distributions are difficult to acquire for this unconventional reservoir type,despite their importance.However,nuclear magnetic resonance(NMR)logging can in principle provide such information via hydrogen relaxation time measurements.Thus,in this paper,NMR response curves(of shale samples)were rigorously mathematically analyzed(with an Expectation Maximization algorithm)and categorized based on the NMR data and their geology,respectively.Thus the number of the NMR peaks,their relaxation times and amplitudes were analyzed to characterize pore size distributions and lithofacies.Seven pore size distribution classes were distinguished;these were verified independently with Pulsed-Neutron Spectrometry(PNS)well-log data.This study thus improves the interpretation of well log data in terms of pore structure and mineralogy of shale reservoirs,and consequently aids in the optimization of shale gas extraction from the subsurface.

Study on sedimentation distribution based on cooperative analysis of geologic-geophysical in less well area: A case study of Suweiyi sandstone in the DB area, Kuqa Depression in Tarim Basin

The Kuqa Depression in Tarim Basin develops fan deltaic,braided river deltaic,and lacustrine sedi-mentation,espeially extensive braided river deltaic sedimentation,in the Cretaceous-Paleogene Sys-tems.However,fine sedimentary pattern of the Kuqa Depression and North Tarim Uplift belt since the Middle Cenozoic still needs to be studied.As a combination zone of the Kuqa Depression and North Tarim Uplift,the sedimentary characteristics of the DB area in the southern margin of the east of the Kuqa depression have been paid more attention.To better understand the sedimentary framework in the Kuqa Depression and North Tarim Uplift in the Mesozoic and Cenozoic,through joint geologic-geophysical study,sedime ntation of sandstone at the bottom of the Paleogene Suweiyi Formation in the DB area and its peripheral area is investigated.Sedimentary facies and sandstone distribution in the area are identified through core observation,component analysis,logging interpretation and seismic inversion.Based on seismic facies analysis,sedimentary facies distribution in the area is delineated.Results show that sandstone at the bottom of the Paleogene Suweiyi Fommation in the DB area and its peripheral area is developed in shore shallow lacustrine beach-bar facies.The beach-bar arenaceous sediments are mainly distnibuted in the southern DB area and the shallow lacustrine mudstone is developed in northern DB area,showing obvious north south di ferentiation charactenistics.

Reflection full waveform inversion

Because of the combination of optimization algorithms and full wave equations, full-waveform inversion(FWI) has become the frontier of the study of seismic exploration and is gradually becoming one of the essential tools for obtaining the Earth interior information. However, the application of conventional FWI to pure reflection data in the absence of a highly accurate starting velocity model is difficult. Compared to other types of seismic waves, reflections carry the information of the deep part of the subsurface. Reflection FWI, therefore, is able to improve the accuracy of imaging the Earth interior further. Here, we demonstrate a means of achieving this successfully by interleaving least-squares RTM with a version of reflection FWI in which the tomographic gradient that is required to update the background macro-model is separated from the reflectivity gradient using the Born approximation during forward modeling. This provides a good update to the macro-model. This approach is then followed by conventional FWI to obtain a final high-fidelity high-resolution result from a poor starting model using only reflection data.Further analysis reveals the high-resolution result is achieved due to a deconvolution imaging condition implicitly used by FWI.

Least-squares reverse-time migration for reflectivity imaging

A least-squares reverse-time migration scheme is presented for reflectivity imaging. Based on an accurate reflection modeling formula, this scheme produces amplitude-preserved stacked reflectivity images with zero phase. Spatial preconditioning, weighting and the Barzilai-Borwein method are applied to speed up the convergence of the least-squares inversion. In addition, this scheme compensates the effect of ghost waves to broaden the bandwidth of the reflectivity images. Furthermore, roughness penalty constraint is used to regularize the inversion, which in turn stabilizes inversion and removes high-wavenumber artifacts and mitigates spatial aliasing. The examples of synthetic and field datasets demonstrate the scheme can generate zerophase reflectivity images with broader bandwidth, higher resolution, fewer artifacts and more reliable amplitudes than conventional reverse-time migration.