arXiv subjects

Cai Liu

Publications and source records attributed to Cai Liu.

At least 19 recordsLinked to original sources

arXiv2026

Tensor Train Decomposition-based 3D Implicit Full Waveform Inversion with Multi-scale Structural Similarity

Three-dimensional full waveform inversion (3DFWI) is a powerful technique for reconstructing high-resolution subsurface velocity models. However, its application is often limited by high memory requirements, computational costs, and sensitivity to cycle skipping. To overcome these challenges, we propose a novel tensor train (TT) decomposition-based 3D implicit full waveform inversion framework (TT-3DIFWI) combined with a multi-scale structural similarity (M-SSIM) objective function. In this framework, the 3D velocity model is represented by TT decomposition as a product of a series of low-rank core tensors. Then, three axis-specific implicit neural network representations (INR) based on one-dimensional vector coordinates as input are constructed to predict these core tensors, rather than directly predicting the velocity model. This INR reparameterization method based on TT decomposition can significantly reduce the memory consumption of INR training while maintaining the accuracy and resolution of the 3D velocity model reconstruction. Meanwhile, the low-rank structure of TT decomposition also ensures the structural consistency of the reconstruction velocity, thereby improving the accuracy and continuity of the inversion result. Furthermore, the M-SSIM objective function can compare the multi-scale structural differences between predicted and observed data, and utilize the ultra-low frequency features to reduce cycle skipping. Numerical experiments on synthetic and challenging land datasets demonstrate that TT-3DIFWI with M-SSIM achieves accurate and continuous velocity reconstruction, even with poor initial models or missing low-frequency data.

physics.geo-ph↗

arXiv2025

Fast ground penetrating radar dual-parameter full waveform inversion method accelerated by hybrid compilation of CUDA kernel function and PyTorch

This study proposes a high-performance dual-parameter full waveform inversion framework (FWI) for ground-penetrating radar (GPR), accelerated through the hybrid compilation of CUDA kernel functions and PyTorch. The method leverages the computational efficiency of GPU programming while preserving the flexibility and usability of Python-based deep learning frameworks. By integrating customized CUDA kernels into PyTorch's automatic differentiation mechanism, the framework enables accurate and efficient inversion of both dielectric permittivity and electrical conductivity. Experimental evaluations on synthetic data and real wavefield data demonstrate that the proposed method achieves dual-parameter FWI for GPR data while maintaining high accuracy. Moreover, the framework is flexible and extensible, supporting optional regularization strategies such as total variation and multi-scale inversion. These features make the proposed approach a practical and scalable framework for rapid GPR-based subsurface imaging in applications including civil engineering, environmental monitoring, and geophysical exploration.

physics.geo-ph↗

arXiv2025

Seismic first-arrival traveltime simulation based on reciprocity-constrained PINN

Simulating seismic first-arrival traveltime plays a crucial role in seismic tomography. First-arrival traveltime simulation relies on solving the eikonal equation. The accuracy of conventional numerical solvers is limited to a finite-difference approximation. In recent years, physics-informed neural networks (PINNs) have been applied to achieve this task. However, traditional PINNs encounter challenges in accurately solving the eikonal equation, especially in cases where the model exhibits directional scaling differences. These challenges result in substantial traveltime prediction errors when the traveling distance is long. To improve the accuracy of PINN in traveltime prediction, we incorporate the reciprocity principle as a constraint into the PINN training framework. Based on the reciprocity principle, which states that the traveltime between two points remains invariant when their roles as source and receiver are exchanged, we propose to apply this principle to multiple source-receiver pairs in PINN-based traveltime prediction. Furthermore, a dynamic weighting mechanism is proposed to balance the contributions of the eikonal equation loss and the reciprocity-constrained loss during the training process. This adaptive weighting evolves dynamically with the training epochs, enhancing the convergency of the training process. Experiments conducted on a simple lens velocity model, the Overthrust velocity model, and a 3D velocity model demonstrate that the introduction of the reciprocity-constrained PINN significantly improves the accuracy of traveltime predictions.

physics.geo-ph↗

arXiv2025

MS_ATpV-FWI: Full Waveform Inversion based on Multi-scale Structural Similarity Index Measure and Anisotropic Total p-Variation Regularization

Full waveform inversion (FWI) is a high-resolution seismic inversion technique popularly used in oil and gas exploration. Traditional FWI employs the $l_2$ norm measurement to minimize the misfit between observed and predicted seismic data. However, when the background velocity is inaccurate or the seismic data lacks low-frequency components, the conventional FWI suffers from cycle skipping, leading to inaccurate inversion results. This paper introduces a multiscale structural similarity index measure (M-SSIM) objective function for FWI. We also incorporate anisotropic total p-variation regularization (ATpV) to further improve the accuracy of FWI. M-SSIM extracts multi-scale structural features of seismic data in terms of both phase and amplitude. These features can reduce the risk of cycle skipping and improve the stability of FWI. Additionally, ATpV applies structural constraints to the velocity gradients, which helps suppress artifacts and preserve the sharp boundaries of geological formations. We propose to use the automatic differentiation (AD) to efficiently and stably optimize this novelly introduced FWI objective function. Both synthetic and field seismic data demonstrate that the proposed method accurately characterizes complex subsurface velocity structures, even when the background velocity is crude, the data lacks low-frequency components, or contains noise.

physics.geo-ph↗

arXiv2025

A new practical and effective source-independent full-waveform inversion with a velocity-distribution supported deep image prior: Applications to two real datasets

Full-waveform inversion (FWI) is an advanced technique for reconstructing high-resolution subsurface physical parameters by progressively minimizing the discrepancy between observed and predicted seismic data. However, conventional FWI encounters challenges in real data applications, primarily due to its conventional objective of direct measurements of the data misfit. Accurate estimation of the source wavelet is essential for effective data fitting, alongside the need for low-frequency data and a reasonable initial model to prevent cycle skipping. Additionally, wave equation solvers often struggle to accurately simulate the amplitude of observed data in real applications. To address these challenges, we introduce a correlation-based source-independent objective function for FWI that aims to mitigate source uncertainty and amplitude dependency, which effectively enhances its practicality for real data applications. We develop a deep-learning framework constrained by this new objective function with a velocity-distribution supported deep image prior, which reparameterizes velocity inversion into trainable parameters within an autoencoder, thereby reducing the nonlinearity in the conventional FWI's objective function. We demonstrate the superiority of our proposed method using synthetic data from benchmark velocity models and, more importantly, two real datasets. These examples highlight its effectiveness and practicality even under challenging conditions, such as missing low frequencies, a crude initial velocity model, and an incorrect source wavelet.

physics.geo-ph↗

arXiv2024

PINNPStomo: Simultaneous P- and S-wave seismic traveltime tomography using physics-informed neural networks with a new factored eikonal equation

Seismic tomography has long been an effective tool for constructing reliable subsurface structures. However, simultaneous inversion of P- and S-wave velocities presents a significant challenge for conventional seismic tomography methods, which depend on numerical algorithms to calculate traveltimes. A physics informed neural network (PINN)-based seismic tomography method (PINNtomo) has been proposed to solve the eikonal equation and construct the velocity model. Leveraging the powerful approximation capabilities of neural networks, we propose extending PINNtomo to perform multiparameter inversion of P- and S-wave velocities jointly, which we refer to as PINNPStomo. In PINNPStomo, we employ two neural networks: one for the P- and S-wave traveltimes, and another for the P- and S-wave velocities. By optimizing the misfits of P- and S-wave first-arrival traveltimes calculated from the eikonal equations, we can obtain the predicted P- and S-wave velocities that determine these traveltimes. Recognizing that the original PINNtomo utilizes a multiplicative factored eikonal equation, which depends on background traveltimes corresponding to a homogeneous velocity at the source location. We propose a new factored eikonal equation for PINNPStomo to eliminate this dependency. The proposed PINNPStomo, incorporating the new factored eikonal equation, demonstrates superior convergence speed and multiparameter inversion accuracy. We validate these improvements using 2D Marmousi and 2D/3D Overthrust elastic velocity models across three different seismic data acquisition geometries.

physics.geo-ph↗

arXiv2024

Examining the possibility of chiral superconductivity in Sr$_2$RuO$_4$ and other compounds via applied supercurrent

One approach to probe the still controversial superconductivity in Sr$_2$RuO$_4$ is to apply external perturbations that break the underlying tetragonal crystalline symmetry. Chiral $p_x+ip_y$ and $d_{xz}+id_{yz}$ states respond to such perturbations in ways that may help to distinguish them from other superconducting pairings. However, past experimental efforts along this line, using uniaxial strains and magnetic fields parallel to the RuO$_2$ plane, have not been able to reach an unambiguous conclusion. In this study, we propose to further examine the possibility of chiral superconducting order in Sr$_2$RuO$_4$ using an alternative tetragonal-symmetry-breaking perturbation -- in-plane supercurrent. We study the superconducting phase diagram as a function of both temperature and the applied supercurrent. Supercurrent generically splits the transition of the two chiral order parameter components, and we show that the splitting can give rise to visible specific heat anomalies. Furthermore, supercurrent parallel and anti-parallel to the unidirectional propagation of the chiral edge modes impact the edge states in different manner. This difference manifests in the tunneling spectrum, thereby providing an additional means to probe the chirality even when the related spontaneous edge current is vanishingly small. Finally, we discuss the distinction of supercurrent responses in non-chiral time-reversal-symmetry-breaking superconducting states. Our proposal can be applied to other candidate chiral superconductors.

cond-mat.supr-con↗

arXiv2023

Seismic traveltime simulation for variable velocity models using physics-informed Fourier neural operator

Seismic traveltime is critical information conveyed by seismic waves, widely utilized in various geophysical applications. Conventionally, the simulation of seismic traveltime involves solving the eikonal equation. However, the efficiency of traditional numerical solvers is hindered, as they are typically capable of simulating seismic traveltime for only a single source at a time. Recently, deep learning tools, particularly physics-informed neural networks (PINNs), have proven effective in simulating seismic traveltimes for multiple sources. Nonetheless, PINNs face challenges such as limited generalization capabilities across different models and difficulties in training convergence. To address these issues, we have developed a method for simulating multi-source seismic traveltimes in variable velocity models using a deep-learning technique, known as the physics-informed Fourier neural operator (PIFNO). The PIFNO-based method for seismic traveltime generation takes both velocity and background traveltime as inputs, generating the perturbation traveltime as the output. This method incorporates a factorized eikonal equation as the loss function and relies solely on physical laws, eliminating the need for labeled training data. We demonstrate that our proposed method is not only effective in calculating seismic traveltimes for velocity models used during training but also shows promising prediction capabilities for test velocity models. We validate these features using velocity models from the OpenFWI dataset.

physics.geo-ph↗

arXiv2022

Intrinsic Magnetic Topological Materials

Topological states of matter possess bulk electronic structures categorized by topological invariants and edge/surface states due to the bulk-boundary correspondence. Topological materials hold great potential in the development of dissipationless spintronics, information storage, and quantum computation, particularly if combined with magnetic order intrinsically or extrinsically. Here, we review the recent progress in the exploration of intrinsic magnetic topological materials, including but not limited to magnetic topological insulators, magnetic topological metals, and magnetic Weyl semimetals. We pay special attention to their characteristic band features such as the gap of topological surface state, gapped Dirac cone induced by magnetization (either bulk or surface), Weyl nodal point/line, and Fermi arc, as well as the exotic transport responses resulting from such band features. We conclude with a brief envision for experimental explorations of new physics or effects by incorporating other orders in intrinsic magnetic topological materials.

cond-mat.mes-hall↗

arXiv2022

Strain tunability of perpendicular magnetic anisotropy in van der Waals ferromagnets VI3

Layered ferromagnets with high coercivity have special applications in nanoscale memory elements in electronic circuits, such as data storage. Therefore, searching for new hard ferromagnets and effectively tuning or enhancing the coercivity are the hottest topics in layered magnets today. Here, we report a strain tunability of perpendicular magnetic anisotropy in van der Waals (vdW) ferromagnets VI3 using magnetic circular dichroism measurements. For an unstrained flake, the M-H curve shows a rectangular-shaped hysteresis loop with perpendicular magnetic anisotropy and a large coercivity (up to 1.775 T at 10 K). Furthermore, the coercivity can be enhanced to a maximum of 2.6 T at 10 K under a 2.9% in-plane tensile strain. Our DFT calculations show that the magnetic anisotropy energy (MAE) can be dramatically increased after applying an in-plain tensile strain, which contributes to the enhancement of coercivity in the VI3 flake. Meanwhile, the strain tunability on the coercivity of CrI3, with a similar crystal structure, is limited. The main reason is the strong spin-orbital coupling in V3+ in VI6 octahedra in comparison with that in Cr3+. The strain tunability of coercivity in VI3 flakes highlights its potential for integration into vdW heterostructures, paving the way toward nanoscale spintronic devices and applications in the future.

cond-mat.mtrl-sci↗

arXiv2022

Realization of Practical Eightfold Fermions and Fourfold van Hove Singularity in TaCo$_2$Te$_2$

Space groups describing the symmetry of lattice structure allow the emergence of fermionic quasiparticles with various degeneracy in the band structure. Theoretical efforts have predicted many materials hosting fermions with the highest degeneracy, i.e., eightfold fermions, yet lacking experimental realization. Here, we explore the band degeneracies in TaCo$_2$Te$_2$ crystals. Through systematic experimental and theoretical analyses, we establish TaCo$_2$Te$_2$ as a nonsymmorphic crystal with negligible spin-orbit coupling (SOC) and long-range magnetic order. These critical properties guarantee the first realization of practical eightfold fermions and fourfold van Hove singularity, as directly observed by photoemission spectroscopy. TaCo$_2$Te$_2$ serves as a topological quantum critical platform, which can be tuned into various magnetic, topologically trivial, and nontrivial phases by adding strain, magnetic field, or SOC. The latter is demonstrated by our first-principles calculations, which show that enhancing SOC in TaCo$_2$Te$_2$ will promote the experimental observation of bulk hourglass fermions. Our results establish TaCo$_2$Te$_2$ as a unique platform to explore states of matter intertwining magnetism, correlation, symmetry, and band topology.

cond-mat.str-el↗

arXiv2022

Muon Spin Relaxation Study of Spin Dynamics on a Kitaev honeycomb material H$_3$LiIr$_2$O$_6$

The vacancy effect in quantum spin liquid (QSL) has been extensively studied. A finite density of random vacancies in the Kitaev model can lead to a pileup of low-energy density of states (DOS), which is generally experimentally determined by a scaling behavior of thermodynamic or magnetization quantities. Here, we report detailed muon spin relaxation ($\mu$SR) results of H$_3$LiIr$_2$O$_6$, a Kitaev QSL candidate with vacancies. The absence of magnetic order is confirmed down to 80 mK, and the spin fluctuations are found to be persistent at low temperatures. Intriguingly, the time-field scaling law of longitudinal-field (LF)-$\mu$SR polarization is observed down to 0.1 K. This indicates a dynamical scaling, whose critical exponent 0.46 is excellently consistent with the scaling behavior of specific heat and magnetization data. All the observations point to the finite DOS with the form $N(E) \sim E^{-0.5}$ , which is expected for the Kitaev QSL in the presence of vacancies. Our {\mu}SR study provides a dynamical fingerprint of the power-law low-energy DOS, and introduces a crucial new insight into the vacancy effect in QSL.

cond-mat.str-el↗

arXiv2022

Type-II Dirac Nodal Lines in double-kagome-layered CsV$_8$Sb$_{12}$

Lorentz-violating type-II Dirac nodal line semimetals (DNLSs), hosting curves of band degeneracy formed by two dispersion branches with the same sign of slope, represent a novel states of matter. While being studied extensively in theory, convincing experimental evidences of type-II DNLSs remain elusive. Recently, Vanadium-based kagome materials have emerged as a fertile ground to study the interplay between lattice symmetry and band topology. In this work, we study the low-energy band structure of double-kagome-layered CsV$_8$Sb$_{12}$ and identify it as a scarce type-II DNLS protected by mirror symmetry. We have observed multiple DNLs consisting of type-II Dirac cones close to or almost at the Fermi level via angle-resolved photoemission spectroscopy (ARPES). First-principle analyses show that spin-orbit coupling only opens a small gap, resulting effectively gapless ARPES spectra, yet generating large spin Berry curvature. These type-II DNLs, together with the interaction between a low-energy van Hove singularity and quasi-1D band as we observed in the same material, suggest CsV$_8$Sb$_{12}$ as an ideal platform for exploring novel transport properties such as chiral anomaly, the Klein tunneling and fractional quantum Hall effect.

cond-mat.str-el↗

arXiv2021

Layer-controlled Ferromagnetism in Atomically Thin CrSiTe$_3$ Flakes

The research on two-dimensional (2D) van der Waals (vdW) ferromagnets has promoted the development of ultrahigh-density and nanoscale data storage. However, intrinsic ferromagnetism in layered magnets is always subject to many factors, such as stacking orders, interlayer couplings, and the number of layers. Here, we report a magnetic transition from soft to hard ferromagnetic behaviors as the thickness of CrSiTe$_3$ flakes decreases down to several nanometers. Phenomenally, in contrast to the negligible hysteresis loop in the bulk counterparts, atomically thin CrSiTe$_3$ shows a rectangular loop with finite magnetization and coercivity as thickness decreases down to ~8 nm, indicative of a single-domain and out-of-plane ferromagnetic order. We find that the stray field is weakened with decreasing thickness, which suppresses the formation of the domain wall. In addition, thickness-dependent ferromagnetic properties also reveal a crossover from 3 dimensional to 2 dimensional Ising ferromagnets at a ~7 nm thickness of CrSiTe$_3$, accompanied by a drop of the Curie temperature from 33 K for bulk to ~17 K for 4 nm sample.

cond-mat.mtrl-sci↗

arXiv2021

Dirac Nodal Lines and Nodal Loops in a Topological Kagome Superconductor CsV$_3$Sb$_5$

The intertwining of charge order, superconductivity and band topology has promoted the AV$_3$Sb$_5$ (A=K, Rb, Cs) family of materials to the center of attention in condensed matter physics. Underlying those mysterious macroscopic properties such as giant anomalous Hall conductivity (AHC) and chiral charge density wave is their nontrivial band topology. While there have been numerous experimental and theoretical works investigating the nontrivial band structure and especially the van Hove singularities, the exact topological phase of this family remains to be clarified. In this work, we identify CsV$_3$Sb$_5$ as a Dirac nodal line semimetal based on the observation of multiple Dirac nodal lines and loops close to the Fermi level. Combining photoemission spectroscopy and density functional theory, we identify two groups of Dirac nodal lines along $k_z$ direction and one group of Dirac nodal loops in the A-H-L plane. These nodal loops are located at the Fermi level within the instrumental resolution limit. Importantly, our first-principle analyses indicate that these nodal loops may be a crucial source of the mysterious giant AHC observed. Our results not only provide a clear picture to categorize the band structure topology of this family of materials, but also suggest the dominant role of topological nodal loops in shaping their transport behavior.

cond-mat.str-el↗

arXiv2021

Doping evolution of superconductivity, charge order and band topology in hole-doped topological kagome superconductors Cs(V$_{1-x}$Ti$_x$)$_3$Sb$_5$

The newly discovered Kagome superconductors $A$V$_3$Sb$_5$ ($A$ = K, Rb, Cs) exhibit superconductivity, charge order, and band topology simultaneously. To explore the intricate interplay between the superconducting and charge orders, we investigate the doping evolution of superconductivity, charge-density-wave (CDW) order, and band topology in doped topological kagome superconductors Cs(V$_{1-x}$Ti$_x$)$_3$Sb$_5$ where the Ti-dopant introduces hole-like charge carriers. Despite the absence of the CDW phase transition in doped compounds even for the lowest doping level of $x=0.047$, the superconductivity survives in all doped samples with enhanced critical temperatures. The high-resolution angle-resolved photoemission spectroscopy (ARPES) measurements reveal that the Ti-dopant in the kagome plane lowers the chemical potential, pushing the van Hove singularity (VHS) at $M$ point above the Fermi level. First-principle simulations corroborate the doping evolution of the band structure observed in ARPES, and affirm that the CDW instability does not occur once the VHS is pushed above the Fermi level, explaining the absence of the CDW ordering in our doped samples Cs(V$_{1-x}$Ti$_x$)$_3$Sb$_5$. Our results demonstrate a competition between the CDW and superconducting orders in the kagome-metal superconductor CsV$_3$Sb$_5$, although the superconductivity is likely inconsequential of the CDW order.

cond-mat.supr-con↗

arXiv2021

Emergence of Quantum Confinement in Topological Kagome Superconductor CsV$_3$Sb$_5$ family

Quantum confinement is a restriction on the motion of electrons in a material to specific region, resulting in discrete energy levels rather than continuous energy bands. In certain materials quantum confinement could dramatically reshape the electronic structure and properties of the surface with respect to the bulk. Here, in the recently discovered kagome superconductor CsV$_3$Sb$_5$ (A=K, Rb, Cs) family of materials, we unveil the dominant role of quantum confinement in determining their surface electronic structure. Combining angle-resolved photoemission spectroscopy (ARPES) measurement and density-functional theory simulation, we report the observations of two-dimensional quantum well states due to the confinement of bulk electron pocket and Dirac cone to the nearly isolated surface layer. The theoretical calculations on the slab model also suggest that the ARPES observed spectra are almost entirely contributed by the top two layers. Our results not only explain the disagreement of band structures between the recent experiments and calculations, but also suggest an equally important role played by quantum confinement, together with strong correlation and band topology, in shaping the electronic properties of this family of materials.

cond-mat.str-el↗

arXiv2021

$LnCu_3(OH)_6Cl_3 (Ln = Gd, Tb, Dy)$: Heavy Lanthanides on Spin-1/2 Kagome Magnets

The spin-1/2 kagome antiferromagnets are key prototype materials for studying frustrated magnetism. Three isostructural kagome antiferromagnets LnCu$_3$(OH)$_6$Cl$_3$ (Ln = Gd, Tb, Dy) have been successfully synthesized by the hydrothermal method. LnCu$_3$(OH)$_6$Cl$_3$ adopts space group $P\overline{3}m1$ and features the layered Cu-kagome lattice with lanthanide Ln$^{3+}$ cations sitting at the center of the hexagons. Although heavy lanthanides (Ln = Gd, Tb, Dy) in LnCu$_3$(OH)$_6$Cl$_3$ provide a large effective magnetic moment and ferromagnetic-like spin correlations compared to light-lanthanides (Nd, Sm, Eu) analogues, Cu-kagome holds an antiferromagnetically ordered state at around 17 K like YCu$_3$(OH)$_6$Cl$_3$.

cond-mat.str-el↗