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Hao Jia

Hao Jia appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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math.APComputation and Languagecond-mat.mes-hallMachine Learningquant-phArtificial Intelligencephysics.chem-ph

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Published work

24 published item(s)

preprint2026arXiv

Advanced Long-term Earth System Forecasting

Reliable long-term forecasting of Earth system dynamics is fundamentally limited by instabilities in current artificial intelligence (AI) models during extended autoregressive simulations. These failures often originate from inherent spectral bias, leading to inadequate representation of critical high-frequency, small-scale processes and subsequent uncontrolled error amplification. Inspired by the nested grids in numerical models used to resolve small scales, we present TritonCast. At the core of its design is a dedicated latent dynamical core, which ensures the long-term stability of the macro-evolution at a coarse scale. An outer structure then fuses this stable trend with fine-grained local details. This design effectively mitigates the spectral bias caused by cross-scale interactions. In atmospheric science, it achieves state-of-the-art accuracy on the WeatherBench 2 benchmark while demonstrating exceptional long-term stability: executing year-long autoregressive global forecasts and completing multi-year climate simulations that span the entire available $2500$-day test period without drift. In oceanography, it extends skillful eddy forecast to $120$ days and exhibits unprecedented zero-shot cross-resolution generalization. Ablation studies reveal that this performance stems from the synergistic interplay of the architecture's core components. TritonCast thus offers a promising pathway towards a new generation of trustworthy, AI-driven simulations. This significant advance has the potential to accelerate discovery in climate and Earth system science, enabling more reliable long-term forecasting and deeper insights into complex geophysical dynamics.

0 citations0 reviewsNo code linkedOpen access
preprint2026arXiv

PnP-Corrector: A Universal Correction Framework for Coupled Spatiotemporal Forecasting

Coupled spatiotemporal forecasting is important for predicting the future evolution of multiple interacting dynamical systems, such as in climate models. However, existing methods are severely constrained by the persistent bottleneck of compounding errors. In coupled systems, errors from each subsystem simulator propagate and amplify one another, a phenomenon we term Reciprocal Error Amplification, leading to a rapid collapse of long-range predictions. To address this challenge, we propose a universal framework called PnP-Corrector (Plug-and-Play Corrector). The core idea of our framework is to decouple the physical simulation from the error correction process: it freezes pre-trained physics simulation engines and exclusively trains a correction agent to proactively counteract the systematic biases emerging from the coupled system. Furthermore, we design an efficient predictive model architecture, DSLCast, to serve as the backbone of this framework. Extensive experiments demonstrate that our method significantly enhances the long-term stability and accuracy of coupled forecasting systems. For instance, in the challenging task of a 300-day global ocean-atmosphere coupled forecast, our PnP-Corrector framework reduces the prediction error of the baseline model by 29% and surpasses state-of-the-art models on several key metrics.

0 citations0 reviewsNo code linkedOpen access
preprint2023arXiv

Multi-Level Variational Spectroscopy using a Programmable Quantum Simulator

Energy spectroscopy is a powerful tool with diverse applications across various disciplines. The advent of programmable digital quantum simulators opens new possibilities for conducting spectroscopy on various models using a single device. Variational quantum-classical algorithms have emerged as a promising approach for achieving such tasks on near-term quantum simulators, despite facing significant quantum and classical resource overheads. Here, we experimentally demonstrate multi-level variational spectroscopy for fundamental many-body Hamiltonians using a superconducting programmable digital quantum simulator. By exploiting symmetries, we effectively reduce circuit depth and optimization parameters allowing us to go beyond the ground state. Combined with the subspace search method, we achieve full spectroscopy for a 4-qubit Heisenberg spin chain, yielding an average deviation of 0.13 between experimental and theoretical energies, assuming unity coupling strength. Our method, when extended to 8-qubit Heisenberg and transverse-field Ising Hamiltonians, successfully determines the three lowest energy levels. In achieving the above, we introduce a circuit-agnostic waveform compilation method that enhances the robustness of our simulator against signal crosstalk. Our study highlights symmetry-assisted resource efficiency in variational quantum algorithms and lays the foundation for practical spectroscopy on near-term quantum simulators, with potential applications in quantum chemistry and condensed matter physics.

0 citations0 reviewsNo code linkedOpen access
preprint2023arXiv

Origin of heterogeneous stripping of lithium in liquid electrolytes

Lithium metal batteries suffer from low cycle life. During discharge, parts of the lithium are not stripped reversibly and remain isolated from the current collector. This isolated lithium is trapped in the insulating remaining solid-electrolyte interphase (SEI) shell and contributes to the capacity loss. However, a fundamental understanding of why isolated lithium forms and how it can be mitigated is lacking. In this article, we perform a combined theoretical and experimental study to understand isolated lithium formation during stripping. We derive a thermodynamic consistent model of lithium dissolution and find that the interaction between lithium and SEI leads to locally preferred stripping and isolated lithium formation. Based on a cryogenic transmission electron microscopy (TEM) setup, we reveal that these local effects are particularly pronounced at kinks of lithium whiskers. We find that lithium stripping can be heterogeneous both on a nanoscale and on a larger scale. Cryo TEM observations confirm our theoretical prediction that isolated lithium occurs less at higher stripping current densities. The origin of isolated lithium lies in local effects, such as heterogeneous SEI, stress fields, or the geometric shape of the deposits. We conclude that in order to mitigate isolated lithium, a uniform lithium morphology during plating and a homogeneous SEI is indispensable.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

AdMix: A Mixed Sample Data Augmentation Method for Neural Machine Translation

In Neural Machine Translation (NMT), data augmentation methods such as back-translation have proven their effectiveness in improving translation performance. In this paper, we propose a novel data augmentation approach for NMT, which is independent of any additional training data. Our approach, AdMix, consists of two parts: 1) introduce faint discrete noise (word replacement, word dropping, word swapping) into the original sentence pairs to form augmented samples; 2) generate new synthetic training data by softly mixing the augmented samples with their original samples in training corpus. Experiments on three translation datasets of different scales show that AdMix achieves signifi cant improvements (1.0 to 2.7 BLEU points) over strong Transformer baseline. When combined with other data augmentation techniques (e.g., back-translation), our approach can obtain further improvements.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Bilingual Terminology Extraction from Comparable E-Commerce Corpora

Bilingual terminologies are important machine translation resources in the field of e-commerce, which are usually either manually translated or automatically extracted from parallel data. The human translation is costly and e-commerce parallel corpora is very scarce. However, the comparable data in different languages in the same commodity field is abundant. In this paper, we propose a novel framework of extracting e-commercial bilingual terminologies from comparable data. Benefiting from the cross-lingual pre-training in e-commerce, our framework can make full use of the deep semantic relationship between source-side terminology and target-side sentence to extract corresponding target terminology. Experimental results on various language pairs show that our approaches achieve significantly better performance than various strong baselines.

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Supervised Contrastive Learning with Structure Inference for Graph Classification

Advanced graph neural networks have shown great potentials in graph classification tasks recently. Different from node classification where node embeddings aggregated from local neighbors can be directly used to learn node labels, graph classification requires a hierarchical accumulation of different levels of topological information to generate discriminative graph embeddings. Still, how to fully explore graph structures and formulate an effective graph classification pipeline remains rudimentary. In this paper, we propose a novel graph neural network based on supervised contrastive learning with structure inference for graph classification. First, we propose a data-driven graph augmentation strategy that can discover additional connections to enhance the existing edge set. Concretely, we resort to a structure inference stage based on diffusion cascades to recover possible connections with high node similarities. Second, to improve the contrastive power of graph neural networks, we propose to use a supervised contrastive loss for graph classification. With the integration of label information, the one-vs-many contrastive learning can be extended to a many-vs-many setting, so that the graph-level embeddings with higher topological similarities will be pulled closer. The supervised contrastive loss and structure inference can be naturally incorporated within the hierarchical graph neural networks where the topological patterns can be fully explored to produce discriminative graph embeddings. Experiment results show the effectiveness of the proposed method compared with recent state-of-the-art methods.

0 citations0 reviewsNo code linkedOpen access
preprint2021arXiv

Linear vortex symmetrization: the spectral density function

We investigate solutions of the 2d incompressible Euler equations, linearized around steady states which are radially decreasing vortices. Our main goal is to understand the smoothness of what we call the spectral density function associated with the linearized operator, which we hope will be a step towards proving full nonlinear asymptotic stability of radially decreasing vortices. The motivation for considering the spectral density function is that it is not possible to describe the vorticity or the stream function in terms of one modulated profile. There are in fact two profiles, both at the level of the physical vorticity and at the level of the stream function. The spectral density function allows us to identify these profiles, and its smoothness leads to pointwise decay of the stream function which is consistent with the decay estimates first proved in Bedrossian-Coti Zelati-Vicol in [5].

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preprint2020arXiv

Bilingual Dictionary Based Neural Machine Translation without Using Parallel Sentences

In this paper, we propose a new task of machine translation (MT), which is based on no parallel sentences but can refer to a ground-truth bilingual dictionary. Motivated by the ability of a monolingual speaker learning to translate via looking up the bilingual dictionary, we propose the task to see how much potential an MT system can attain using the bilingual dictionary and large scale monolingual corpora, while is independent on parallel sentences. We propose anchored training (AT) to tackle the task. AT uses the bilingual dictionary to establish anchoring points for closing the gap between source language and target language. Experiments on various language pairs show that our approaches are significantly better than various baselines, including dictionary-based word-by-word translation, dictionary-supervised cross-lingual word embedding transformation, and unsupervised MT. On distant language pairs that are hard for unsupervised MT to perform well, AT performs remarkably better, achieving performances comparable to supervised SMT trained on more than 4M parallel sentences.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Nonlinear inviscid damping near monotonic shear flows

We prove nonlinear asymptotic stability of a large class of monotonic shear flows among solutions of the 2D Euler equations in the channel $\mathbb{T}\times[0,1]$. More precisely, we consider shear flows $(b(y),0)$ given by a function $b$ which is Gevrey smooth, strictly increasing, and linear outside a compact subset of the interval $(0,1)$ (to avoid boundary contributions which are incompatible with inviscid damping). We also assume that the associated linearized operator satisfies a suitable spectral condition, which is needed to prove linear inviscid damping. Under these assumptions, we show that if $u$ is a solution which is a small and Gevrey smooth perturbation of such a shear flow $(b(y),0)$ at time $t=0$, then the velocity field $u$ converges strongly to a nearby shear flow as the time goes to infinity. This is the first nonlinear asymptotic stability result for Euler equations around general steady solutions for which the linearized flow cannot be explicitly solved.

0 citations0 reviewsNo code linkedOpen access
preprint2020arXiv

Quantum Control via Stimulated Raman User-defined Passage

Stimulated Raman adiabatic passage (STIRAP) is a widely-used technique of coherent state-to-state manipulation for many applications in physics, chemistry, and beyond. The adiabatic evolution of the state involved in STIRAP, called adiabatic passage, guarantees its robustness against control errors, but also leads to problems of low efficiency and decoherence. Here we propose and experimentally demonstrate an alternative approach, termed stimulated Raman "user-defined" passage (STIRUP), where a parameterized state is employed for constructing desired evolutions to replace the adiabatic passage in STIRAP. The user-defined passages can be flexibly designed for optimizing different objectives for different tasks, e.g. minimizing leakage error. To experimentally benchmark its performance, we apply STIRUP to the task of coherent state transfer in a superconducting Xmon qutrit. We found that STIRUP completed the transfer more then four times faster than STIRAP with enhanced robustness, and achieved a fidelity of 99.5%, which is the highest among all recent experiments based on STIRAP and its variants. In practice, STIRUP differs from STIRAP only in the design of driving pulses; therefore, most existing applications of STIRAP can be readily implemented with STIRUP.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Large-Scale Arrays of Single- and Few-Layer MoS2 Nanomechanical Resonators

We report on fabrication of large-scale arrays of suspended molybdenum disulfide (MoS2) atomic layers, as two-dimensional (2D) MoS2 nanomechanical resonators. We employ a water-assisted lift-off process to release chemical vapor deposited (CVD) MoS2 atomic layers from a donor substrate, followed by an all-dry transfer onto microtrench arrays. The resultant large arrays of suspended single- and few-layer MoS2 drumhead resonators (0.5 to 2um in diameter) offer fundamental resonances (f_0) in the very high frequency (VHF) band (up to ~120MHz) and excellent figures-of-merit up to f_0*Q ~ 3*10^10Hz. A stretched circular diaphragm model allows us to estimate low pre-tension levels of typically ~15mN/m in these devices. Compared to previous approaches, our transfer process features high yield and uniformity with minimal liquid and chemical exposure (only involving DI water), resulting in high-quality MoS2 crystals and exceptional device performance and homogeneity; and our process is readily applicable to other 2D materials.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Resolving and Tuning Mechanical Anisotropy in Black Phosphorus via Nanomechanical Multimode Resonance Spectromicroscopy

Black phosphorus (P) has emerged as a layered semiconductor with a unique crystal structure featuring corrugated atomic layers and strong in-plane anisotropy in its physical properties. Here, we demonstrate that the crystal orientation and mechanical anisotropy in free-standing black P thin layers can be precisely determined by spatially resolved multimode nanomechanical resonances. This offers a new means for resolving important crystal orientation and anisotropy in black P device platforms in situ beyond conventional optical and electrical calibration techniques. Furthermore, we show that electrostatic-gating-induced straining can continuously tune the mechanical anisotropic effects on multimode resonances in black P electromechanical devices. Combined with finite element modeling (FEM), we also determine the Young's moduli of multilayer black P to be 116.1 and 46.5 GPa in the zigzag and armchair directions, respectively.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Soliton resolution along a sequence of times with dispersive error for type II singular solutions to focusing energy critical wave equation

In this paper, we study the soliton resolution conjecture for Type II singular solutions $\overrightarrow{u}(t)$ to the focusing energy critical wave equation in $R^d\times [0,T_+)$, with $3\leq d\leq 5$. Suppose that $u$ has a singularity at $(x,t)=(0,T_+)$, we show that along a sequence of times $t_n\uparrow T_+$ and in a neighborhood of $(0,T_+)$, $\overrightarrow{u}(t_n)$ can be decomposed as the sum of a regular part in the energy space, a finite combination of modulated solitons (translation, scaling and Lorentz transform of steady states) and a residue term which goes to zero in the Strichartz norm. In addition, the residue term is asymptotically radial and can concentrate energy only in a thin annulus near $|x|=T_+-t_n$. Our main tools include a Morawetz estimate, similar to the one used for wave maps, and the use of a virial identity to eliminate dispersive energy in $|x|<λ(T_+ -t_n)$ for any $λ\in (0,1)$.

0 citations0 reviewsNo code linkedOpen access
preprint2016arXiv

Universality of blow up profile for small blow up solutions to the energy critical wave map equation

In this paper we introduce the channel of energy argument to the study of energy critical wave maps into the sphere. More precisely, we prove a channel of energy type inequality for small energy wave maps, and as an application we show that for a wave map that has energy just above the degree one harmonic maps and that blows up in finite time, the solution asymptotically de-couples into a regular part plus a traveling wave with small momentum, in the energy space. In particular, the only possible form of energy concentration is through the concentration of traveling waves. This is often called quantization of energy at blow up. We also give a brief review of important background results in the subcritical and critical regularity theory for the two dimensional wave maps.

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preprint2015arXiv

Asymptotic decomposition for semilinear wave and equivariant wave map equations

In this paper we give a unified proof to the soliton resolution conjecture along a sequence of times, for the semilinear focusing energy critical wave equations in the radial case and two dimensional equivariant wave map equations, including the four dimensional radial Yang Mills equation, without using outer energy type inequalities. Such inequalities have played a crucial role in previous works with similar results. Roughly speaking, we prove that along a sequence of times approaching the maximal time of existence, the solution decouples to a sum of rescaled solitons and a term vanishing in the energy space, plus a free radiation term in the global case or a regular part in the finite time blow up case. The main difficulty is that in general (for instance for the radial four dimensional Yang Mills case and the radial six dimensional semilinear wave case) we do not have a favorable outer energy inequality for the associated linear wave equations. Our main new input is the simultaneous use of two virial identities.

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preprint2015arXiv

Black Phosphorus Nanoelectromechanical Resonators Vibrating at Very High Frequencies

We report on experimental demonstration of a new type of nanoelectromechanical resonators based on black phosphorus crystals. Facilitated by a highly efficient dry transfer technique, crystalline black phosphorus flakes are harnessed to enable drumhead resonators vibrating at high and very high frequencies (HF and VHF bands, up to ~100MHz). We investigate the resonant vibrational responses from the black phosphorus crystals by devising both electrical and optical excitation schemes, in addition to measuring the undriven thermomechanical motions in these suspended nanostructures. Flakes with thicknesses from ~200nm down to ~20nm clearly exhibit elastic characteristics transitioning from the plate to the membrane regime. Both frequency- and time-domain measurements of the nanomechanical resonances show that very thin black phosphorus crystals hold interesting promises for moveable and vibratory devices, and for semiconductor transducers where high-speed mechanical motions could be coupled to the attractive electronic and optoelectronic properties of black phosphorus.

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preprint2015arXiv

Generic and non-generic behavior of solutions to the defocusing energy critical wave equation with potential in the radial case

In this paper, we continue our study [16] on the long time dynamics of radial solutions to defocusing energy critical wave equation with a trapping radial potential in 3 + 1 dimensions. For generic radial potentials (in the topological sense) there are only finitely many steady states which might be either stable or unstable. We first observe that there can be stable excited states (i.e., a steady state which is not the ground state) if the potential is large and attractive, although all small excited states are unstable. We prove that the set of initial data for which solutions scatter to any one unstable excited state forms a finite co-dimensional connected $C^1$ manifold in energy space. This amounts to the construction of the global path-connected, and unique, center-stable manifold associated with, but not necessarily close to, any unstable steady state. In particular, the set of data for which solutions scatter to unstable states has empty interior in the energy space, and generic radial solutions scatter to one of the stable steady states. Our main tools are (i) near any given finite energy radial initial data $(u_0,u_1)$ for which the solution $u(t)$ scatters to some unstable steady state $ϕ$ we construct a $C^1$ manifold containing $(u_0,u_1)$ with the property that any solution starting on the manifold scatters to $ϕ$; moreover, any solution remaining near the manifold for all positive times lies on the manifold (ii) an exterior energy inequality from [9,10,16]. The latter is used to obtain a result in the spirit of the one-pass theorem [22], albeit with completely different techniques

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preprint2014arXiv

Long time dynamics of defocusing energy critical 3 + 1 dimensional wave equation with potential in the radial case

Using channel of energy inequalities developed by T.Duyckaerts, C.Kenig and F.Merle, we prove that, modulo a free radiation, any finite energy radial solution to the defocusing energy critical wave equation with radial potential in 3 + 1 dimensions converges to the set of steady states as time goes to infinity. For generic potentials we prove there are only finitely many steady states, and in this case modulo some free radiation the solution converges to one steady state as time goes to infinity.

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preprint2013arXiv

Are the incompressible 3d Navier-Stokes equations locally ill-posed in the natural energy space?

An important open problem in the theory of the Navier-Stokes equations is the uniqueness of the Leray-Hopf weak solutions with $L^2$ initial data. In this paper we give sufficient conditions for non-uniqueness in terms of spectral properties of a natural linear operator associated to scale-invariant solutions recently constructed in \cite{JiaSverak}. If the spectral conditions are satisfied, non-uniqueness and ill-posedness can appear for quite benign compactly supported data, just at the borderline of applicability of the classical perturbation theory. The verification of the spectral conditions seems to be approachable by relatively straightforward numerical simulations which involve only smooth functions.

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preprint2012arXiv

Local-in-space estimates near initial time for weak solutions of the Navier-Stokes equations and forward self-similar solutions

We show that the classical Cauchy problem for the incompressible 3d Navier-Stokes equations with $(-1)$-homogeneous initial data has a global scale-invariant solution which is smooth for positive times. Our main technical tools are local-in-space regularity estimates near the initial time, which are of independent interest.

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