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Showing papers in "Bulletin of the American Physical Society in 2018"


Journal Article
TL;DR: In this article, the effects of the twist angle between different layers in a van der Waals heterostructure have been investigated and it was shown that when this angle is close to the magic angle, the electronic band structure near zero Fermi energy becomes flat, owing to strong interlayer coupling.
Abstract: A van der Waals heterostructure is a type of metamaterial that consists of vertically stacked two-dimensional building blocks held together by the van der Waals forces between the layers. This design means that the properties of van der Waals heterostructures can be engineered precisely, even more so than those of two-dimensional materials. One such property is the 'twist' angle between different layers in the heterostructure. This angle has a crucial role in the electronic properties of van der Waals heterostructures, but does not have a direct analogue in other types of heterostructure, such as semiconductors grown using molecular beam epitaxy. For small twist angles, the moire pattern that is produced by the lattice misorientation between the two-dimensional layers creates long-range modulation of the stacking order. So far, studies of the effects of the twist angle in van der Waals heterostructures have concentrated mostly on heterostructures consisting of monolayer graphene on top of hexagonal boron nitride, which exhibit relatively weak interlayer interaction owing to the large bandgap in hexagonal boron nitride. Here we study a heterostructure consisting of bilayer graphene, in which the two graphene layers are twisted relative to each other by a certain angle. We show experimentally that, as predicted theoretically, when this angle is close to the 'magic' angle the electronic band structure near zero Fermi energy becomes flat, owing to strong interlayer coupling. These flat bands exhibit insulating states at half-filling, which are not expected in the absence of correlations between electrons. We show that these correlated states at half-filling are consistent with Mott-like insulator states, which can arise from electrons being localized in the superlattice that is induced by the moire pattern. These properties of magic-angle-twisted bilayer graphene heterostructures suggest that these materials could be used to study other exotic many-body quantum phases in two dimensions in the absence of a magnetic field. The accessibility of the flat bands through electrical tunability and the bandwidth tunability through the twist angle could pave the way towards more exotic correlated systems, such as unconventional superconductors and quantum spin liquids.

1,961 citations


Journal Article
TL;DR: In this paper, the authors developed the topological band theory for systems described by non-Hermitian Hamiltonians, whose energy spectra are generally complex, and classified gapped bands in one and two dimensions by explicitly finding their topological invariants.
Abstract: We develop the topological band theory for systems described by non-Hermitian Hamiltonians, whose energy spectra are generally complex. After generalizing the notion of gapped band structures to the non-Hermitian case, we classify ``gapped'' bands in one and two dimensions by explicitly finding their topological invariants. We find nontrivial generalizations of the Chern number in two dimensions, and a new classification in one dimension, whose topology is determined by the energy dispersion rather than the energy eigenstates. We then study the bulk-edge correspondence and the topological phase transition in two dimensions. Different from the Hermitian case, the transition generically involves an extended intermediate phase with complex-energy band degeneracies at isolated ``exceptional points'' in momentum space. We also systematically classify all types of band degeneracies.

435 citations


Journal Article
TL;DR: In this paper, the surface of the iron-based superconductor FeTe0.55Se0.45 has been shown to be topologically superconducting, providing a simple and possibly high-temperature platform for realizing Majorana states.
Abstract: A topological superconductor A promising path toward topological quantum computing involves exotic quasiparticles called the Majorana bound states (MBSs). MBSs have been observed in heterostructures that require careful nanofabrication, but the complexity of such systems makes further progress tricky. Zhang et al. identified a topological superconductor in which MBSs may be observed in a simpler way by looking into the cores of vortices induced by an external magnetic field. Using angle-resolved photoemission, the researchers found that the surface of the iron superconductor FeTe0.55Se0.45 satisfies the required conditions for topological superconductivity. Science, this issue p. 182 Angle-resolved photoemission spectroscopy indicates that FeTe0.55Se0.45 harbors Dirac-cone–type spin-helical surface states. Topological superconductors are predicted to host exotic Majorana states that obey non-Abelian statistics and can be used to implement a topological quantum computer. Most of the proposed topological superconductors are realized in difficult-to-fabricate heterostructures at very low temperatures. By using high-resolution spin-resolved and angle-resolved photoelectron spectroscopy, we find that the iron-based superconductor FeTe1–xSex (x = 0.45; superconducting transition temperature Tc = 14.5 kelvin) hosts Dirac-cone–type spin-helical surface states at the Fermi level; the surface states exhibit an s-wave superconducting gap below Tc. Our study shows that the surface states of FeTe0.55Se0.45 are topologically superconducting, providing a simple and possibly high-temperature platform for realizing Majorana states.

347 citations


Journal Article
TL;DR: In this article, a gradient-domain machine learning (sGDML) model is proposed to construct flexible molecular force fields from high-level ab initio calculations by incorporating spatial and temporal physical symmetries into a sGDML model.
Abstract: Molecular dynamics (MD) simulations employing classical force fields constitute the cornerstone of contemporary atomistic modeling in chemistry, biology, and materials science. However, the predictive power of these simulations is only as good as the underlying interatomic potential. Classical potentials often fail to faithfully capture key quantum effects in molecules and materials. Here we enable the direct construction of flexible molecular force fields from high-level ab initio calculations by incorporating spatial and temporal physical symmetries into a gradient-domain machine learning (sGDML) model in an automatic data-driven way. The developed sGDML approach faithfully reproduces global force fields at quantum-chemical CCSD(T) level of accuracy and allows converged molecular dynamics simulations with fully quantized electrons and nuclei. We present MD simulations, for flexible molecules with up to a few dozen atoms and provide insights into the dynamical behavior of these molecules. Our approach provides the key missing ingredient for achieving spectroscopic accuracy in molecular simulations.

312 citations


Journal Article
TL;DR: Theoretically, topological insulators are topological topologists that are insulating in their interior and on their surfaces but have conducting channels at corners or along edges as discussed by the authors.
Abstract: Theorists have discovered topological insulators that are insulating in their interior and on their surfaces but have conducting channels at corners or along edges.

301 citations


Journal Article
TL;DR: D deterministically achieve a two-dimensional lattice of quantum emitters in an atomically thin semiconductor and achieves near unity emitter creation probability and a mean positioning accuracy of 120±32 nm, which may be improved with further optimization of the nanopillar dimensions.

273 citations


Journal Article
TL;DR: This work introduces a scheme for molecular simulations, the deep potential molecular dynamics (DPMD) method, based on a many-body potential and interatomic forces generated by a carefully crafted deep neural network trained with ab initio data.
Abstract: We introduce a scheme for molecular simulations, the deep potential molecular dynamics (DPMD) method, based on a many-body potential and interatomic forces generated by a carefully crafted deep neural network trained with ab initio data. The neural network model preserves all the natural symmetries in the problem. It is first-principles based in the sense that there are no ad hoc components aside from the network model. We show that the proposed scheme provides an efficient and accurate protocol in a variety of systems, including bulk materials and molecules. In all these cases, DPMD gives results that are essentially indistinguishable from the original data, at a cost that scales linearly with system size.

254 citations



Journal Article
TL;DR: The North American Nanohertz Observatory for Gravitational Waves (NANOW) is a collaboration of researchers who are actively engaged in using North American radio telescopes to detect and study gravitational waves (GWs) via pulsar timing.
Abstract: The North American Nanohertz Observatory for Gravitational Waves is a collaboration of researchers who are actively engaged in using North American radio telescopes to detect and study gravitational waves (GWs) via pulsar timing. To achieve this goal, we regularly observe millisecond pulsars with the Arecibo and Green Bank telescopes and develop and implement new instrumentation and algorithms for searching for and observing pulsars, calculating arrival times, understanding and correcting for propagation delays and sources of noise in our data and detecting and characterizing a variety of GW sources. We collaborate on these activities with colleagues in the International Pulsar Timing Array. We also educate students of all levels and the public about the detection and study of GWs via pulsar timing.

218 citations


Journal Article
TL;DR: It is demonstrated that local electric fields can be used to switch reversibly between a magnetic skyrmion and the ferromagnetic state, and the direction of the electric field directly determines the final state, establishing the possibility to combine electric-field writing with the recently envisaged skyrMion racetrack-type memories.

209 citations



Journal Article
TL;DR: This work establishes a system with continuous symmetry-breaking properties, associated collective excitations and superfluid behaviour, and observes the predicted density modulation of this stripe phase using Bragg reflection while maintaining a sharp momentum distribution.
Abstract: Spin–orbit coupling in Bose–Einstein condensates creates a density modulation, which is a stripe phase with supersolid properties. Supersolids exhibit long-range order, just like normal solids, while simultaneously displaying superfluid properties. This state of matter has been extremely difficult to generate and previous results that have suggested supersolidity in helium are yet to be unambiguously verified. Here, Jun-Ru Li and colleagues create a special stripe phase in a one-dimensional spin–orbit-coupled Bose–Einstein condensate and observe some of the predicted supersolid properties. They show that this stripe phase has long-range order in one direction, like a solid, while retaining a sharp momentum distribution, like a superfluid. The authors suggest that these results could be built upon to enable the demonstration of other exotic condensed matter effects, related to disorder and vortex creation. Elsewhere in this issue, Tilman Esslinger and colleagues couple a Bose–Einstein condensate of atoms to two optical cavities and observe the breaking of continuous translational symmetry along one direction. Supersolidity combines superfluid flow with long-range spatial periodicity of solids1, two properties that are often mutually exclusive. The original discussion of quantum crystals2 and supersolidity focused on solid 4He and triggered extensive experimental efforts3,4 that, instead of supersolidity, revealed exotic phenomena including quantum plasticity and mass supertransport4. The concept of supersolidity was then generalized from quantum crystals to other superfluid systems that break continuous translational symmetry. Bose–Einstein condensates with spin–orbit coupling are predicted to possess a stripe phase5,6,7 with supersolid properties8,9. Despite several recent studies of the miscibility of the spin components of such a condensate10,11,12, the presence of stripes has not been detected. Here we observe the predicted density modulation of this stripe phase using Bragg reflection (which provides evidence for spontaneous long-range order in one direction) while maintaining a sharp momentum distribution (the hallmark of superfluid Bose–Einstein condensates). Our work thus establishes a system with continuous symmetry-breaking properties, associated collective excitations and superfluid behaviour.

Journal Article
TL;DR: In situ Raman and ultraviolet-visible spectroscopy alongside spectroelectrochemistry and quantum chemical calculations demonstrate that the redox state of the ligands determines the switching states of the device whereas the counterions control the hysteresis, which may accelerate the technological deployment of organic resistive memories.
Abstract: Non-volatile memories will play a decisive role in the next generation of digital technology. Flash memories are currently the key player in the field, yet they fail to meet the commercial demands of scalability and endurance. Resistive memory devices, and in particular memories based on low-cost, solution-processable and chemically tunable organic materials, are promising alternatives explored by the industry. However, to date, they have been lacking the performance and mechanistic understanding required for commercial translation. Here we report a resistive memory device based on a spin-coated active layer of a transition-metal complex, which shows high reproducibility (∼350 devices), fast switching (≤30 ns), excellent endurance (∼1012 cycles), stability (>106 s) and scalability (down to ∼60 nm2). In situ Raman and ultraviolet-visible spectroscopy alongside spectroelectrochemistry and quantum chemical calculations demonstrate that the redox state of the ligands determines the switching states of the device whereas the counterions control the hysteresis. This insight may accelerate the technological deployment of organic resistive memories.

Journal Article
TL;DR: In this paper, the spin cycloid of a multiferroic bismuth ferrite (BiFeO3) thin film was used for real-time visualization of non-collinear spin order in a magnetic thin film at room temperature.
Abstract: Although ferromagnets have many applications, their large magnetization and the resulting energy cost for switching magnetic moments bring into question their suitability for reliable low-power spintronic devices. Non-collinear antiferromagnetic systems do not suffer from this problem, and often have extra functionalities: non-collinear spin order may break space-inversion symmetry and thus allow electric-field control of magnetism, or may produce emergent spin–orbit effects that enable efficient spin–charge interconversion. To harness these traits for next-generation spintronics, the nanoscale control and imaging capabilities that are now routine for ferromagnets must be developed for antiferromagnetic systems. Here, using a non-invasive, scanning single-spin magnetometer based on a nitrogen–vacancy defect in diamond, we demonstrate real-space visualization of non-collinear antiferromagnetic order in a magnetic thin film at room temperature. We image the spin cycloid of a multiferroic bismuth ferrite (BiFeO3) thin film and extract a period of about 70 nanometres, consistent with values determined by macroscopic diffraction. In addition, we take advantage of the magnetoelectric coupling present in BiFeO3 to manipulate the cycloid propagation direction by an electric field. Besides highlighting the potential of nitrogen–vacancy magnetometry for imaging complex antiferromagnetic orders at the nanoscale, these results demonstrate how BiFeO3 can be used in the design of reconfigurable nanoscale spin textures.

Journal Article
TL;DR: In this article, the authors demonstrate a strong interface between single quantum emitters and topological photonic states and demonstrate the chiral emission of a quantum emitter into these modes and establish their robustness against sharp bends.
Abstract: The application of topology in optics has led to a new paradigm in developing photonic devices with robust properties against disorder Although considerable progress on topological phenomena has been achieved in the classical domain, the realization of strong light-matter coupling in the quantum domain remains unexplored We demonstrate a strong interface between single quantum emitters and topological photonic states Our approach creates robust counterpropagating edge states at the boundary of two distinct topological photonic crystals We demonstrate the chiral emission of a quantum emitter into these modes and establish their robustness against sharp bends This approach may enable the development of quantum optics devices with built-in protection, with potential applications in quantum simulation and sensing

Journal Article
TL;DR: The results show the effectiveness of materials development through state-of-the-art machine-learning techniques by identifying functional inorganic materials.

Journal Article
TL;DR: It is demonstrated for the first time that machine learning can detect and estimate the true parameters of real events observed by LIGO, and achieves similar sensitivities and lower errors compared to matched-filtering while being far more computationally efficient and more resilient to glitches.
Abstract: The recent Nobel-prize-winning detections of gravitational waves from merging black holes and the subsequent detection of the collision of two neutron stars in coincidence with electromagnetic observations have inaugurated a new era of multimessenger astrophysics. To enhance the scope of this emergent field of science, we pioneered the use of deep learning with convolutional neural networks, that take time-series inputs, for rapid detection and characterization of gravitational wave signals. This approach, Deep Filtering , was initially demonstrated using simulated LIGO noise. In this article, we present the extension of Deep Filtering using real data from LIGO, for both detection and parameter estimation of gravitational waves from binary black hole mergers using continuous data streams from multiple LIGO detectors. We demonstrate for the first time that machine learning can detect and estimate the true parameters of real events observed by LIGO. Our results show that Deep Filtering achieves similar sensitivities and lower errors compared to matched-filtering while being far more computationally efficient and more resilient to glitches, allowing real-time processing of weak time-series signals in non-stationary non-Gaussian noise with minimal resources, and also enables the detection of new classes of gravitational wave sources that may go unnoticed with existing detection algorithms. This unified framework for data analysis is ideally suited to enable coincident detection campaigns of gravitational waves and their multimessenger counterparts in real-time.

Journal Article
TL;DR: This Letter fabricate monolayer MoS2/few-layer graphene hybrid spin valves and demonstrates, for the first time, the opto-valleytronic spin injection across a TMD/graphene interface, which paves the way for multifunctional 2D spintronic devices for memory and logic applications.
Abstract: Two-dimensional (2D) materials provide a unique platform for spintronics and valleytronics due to the ability to combine vastly different functionalities into one vertically stacked heterostructure, where the strengths of each of the constituent materials can compensate for the weaknesses of the others. Graphene has been demonstrated to be an exceptional material for spin transport at room temperature; however, it lacks a coupling of the spin and optical degrees of freedom. In contrast, spin/valley polarization can be efficiently generated in monolayer transition metal dichalcogenides (TMD) such as MoS2 via absorption of circularly polarized photons, but lateral spin or valley transport has not been realized at room temperature. In this Letter, we fabricate monolayer MoS2/few-layer graphene hybrid spin valves and demonstrate, for the first time, the opto-valleytronic spin injection across a TMD/graphene interface. We observe that the magnitude and direction of spin polarization is controlled by both helicity and photon energy. In addition, Hanle spin precession measurements confirm optical spin injection, spin transport, and electrical detection up to room temperature. Finally, analysis by a one-dimensional drift-diffusion model quantifies the optically injected spin current and the spin transport parameters. Our results demonstrate a 2D spintronic/valleytronic system that achieves optical spin injection and lateral spin transport at room temperature in a single device, which paves the way for multifunctional 2D spintronic devices for memory and logic applications.

Journal Article
TL;DR: Molecular simulations with a recently proposed nonempirical quantum mechanical approach (the SCAN density functional) yield an excellent description of the structural, electronic, and dynamic properties of liquid water.
Abstract: Water is of the utmost importance for life and technology. However, a genuinely predictive ab initio model of water has eluded scientists. We demonstrate that a fully ab initio approach, relying on the strongly constrained and appropriately normed (SCAN) density functional, provides such a description of water. SCAN accurately describes the balance among covalent bonds, hydrogen bonds, and van der Waals interactions that dictates the structure and dynamics of liquid water. Notably, SCAN captures the density difference between water and ice Ih at ambient conditions, as well as many important structural, electronic, and dynamic properties of liquid water. These successful predictions of the versatile SCAN functional open the gates to study complex processes in aqueous phase chemistry and the interactions of water with other materials in an efficient, accurate, and predictive, ab initio manner.

Journal Article
TL;DR: It is shown that parametric coupling techniques can be used to generate selective entangling interactions for multi-qubit processors and offer a path to a scalable architecture with high selectivity and low cross-talk.
Abstract: Harnessing techniques from analog signal processing, we establish a new path for large-scale quantum computation. We show that parametric coupling techniques can be used to generate selective entangling interactions for multi-qubit processors. By inducing coherent population exchange between adjacent qubits under frequency modulation, we implement a universal gate set for a linear array of four superconducting qubits. An average process fidelity of ℱ = 93% is estimated for three two-qubit gates via quantum process tomography. We establish the suitability of these techniques for computation by preparing a four-qubit maximally entangled state and comparing the estimated state fidelity with the expected performance of the individual entangling gates. In addition, we prepare an eight-qubit register in all possible bitstring permutations and monitor the fidelity of a two-qubit gate across one pair of these qubits. Across all these permutations, an average fidelity of ℱ = 91.6 ± 2.6% is observed. These results thus offer a path to a scalable architecture with high selectivity and low cross-talk.

Journal Article
TL;DR: In this article, the authors used the National Science Foundation (NSF) under grant numbers NSF DMR-09-29966, DMR09-01907, D MR-1401410, and D MMR-1401449, and by the Deutsche Forschungsgemeinschaft under grant number FOR-960.
Abstract: This work has been supported by the National Science Foundation under grant numbers NSF DMR-09-29966, DMR-09-01907, DMR-1401410, and DMR-1401449, and by the Deutsche Forschungsgemeinschaft under grant number FOR-960. Part of this work has been supported by the National Science Foundation under Grant. No. PHYS-1066293 and the hospitality of the Aspen Center for Physics.

Journal Article
TL;DR: A feasible solution for producing structural colors inspired by bird feathers is demonstrated using a one-pot reverse emulsion process and with the combination of only two ingredients, synthetic melanin and silica, it can generate a full spectrum of colors.

Journal Article
TL;DR: In this paper, the authors present a theory of optical absorption by interlayer excitons in a heterobilayer formed from transition metal dichalcogenides, which accounts for the presence of small relative rotations that produce a momentum shift between electron and hole bands located in different layers and a moir\'e pattern in real space.
Abstract: We present a theory of optical absorption by interlayer excitons in a heterobilayer formed from transition metal dichalcogenides. The theory accounts for the presence of small relative rotations that produce a momentum shift between electron and hole bands located in different layers, and a moir\'e pattern in real space. Because of the momentum shift, the optically active interlayer excitons are located at the moir\'e Brillouin zone's corners, instead of at its center, and would have elliptical optical selection rules if the individual layers were translationally invariant. We show that the exciton moir\'e potential energy restores circular optical selection rules by coupling excitons with different center of mass momenta. A variety of interlayer excitons with both senses of circular optical activity, and energies that are tunable by twist angle, are present at each valley. The lowest energy exciton states are generally localized near the exciton potential energy minima. We discuss the possibility of using the moir\'e pattern to achieve scalable two-dimensional arrays of nearly identical quantum dots.


Journal Article
TL;DR: In this article, several machine learning schemes are developed to model the critical temperatures (Tc) of the 12,000+ known superconductors available via the SuperCon database.
Abstract: Superconductivity has been the focus of enormous research effort since its discovery more than a century ago. Yet, some features of this unique phenomenon remain poorly understood; prime among these is the connection between superconductivity and chemical/structural properties of materials. To bridge the gap, several machine learning schemes are developed herein to model the critical temperatures (Tc) of the 12,000+ known superconductors available via the SuperCon database. Materials are first divided into two classes based on their Tc values, above and below 10 K, and a classification model predicting this label is trained. The model uses coarse-grained features based only on the chemical compositions. It shows strong predictive power, with out-of-sample accuracy of about 92%. Separate regression models are developed to predict the values of Tc for cuprate, iron-based, and low-T c compounds. These models also demonstrate good performance, with learned predictors offering potential insights into the mechanisms behind superconductivity in different families of materials. To improve the accuracy and interpretability of these models, new features are incorporated using materials data from the AFLOW Online Repositories. Finally, the classification and regression models are combined into a single-integrated pipeline and employed to search the entire Inorganic Crystallographic Structure Database (ICSD) for potential new superconductors. We identify >30 non-cuprate and non-iron-based oxides as candidate materials. Machine learning schemes are developed to model the superconducting transition temperature of over 12,000 compounds with good accuracy. A team led by Valentin Stanev from the University of Maryland at College Park and including researchers from Duke University and NIST develops several machine learning schemes to model the critical temperature (Tc) of over 12,000 known superconductors and candidate materials. They first train a classification model based only on the chemical compositions to categorize the known superconductors according to whether their Tc is above or below 10 K. Then they develop regression models to predict the values of Tc for various compounds. The accuracy of these models is further improved by including data from the AFLOW Online Repositories. They combine the classification and regression models into a single-integrated pipeline to search the entire Inorganic Crystallographic Structure Database and predict more than 30 new candidate superconductors.

Journal Article
TL;DR: In this article, two distinct emission peaks separated by 24 meV from an interlayer exciton (ILE) were resolved in a MoSe2/WSe2 heterostructure fabricated using state-of-the-art preparation techniques.
Abstract: An emerging class of semiconductor heterostructures involves stacking discrete monolayers such as transition metal dichalcogenides (TMDs) to form van der Waals heterostructures. In these structures, it is possible to create interlayer excitons (ILEs), spatially indirect, bound electron-hole pairs with the electron in one TMD layer and the hole in an adjacent layer. We are able to clearly resolve two distinct emission peaks separated by 24 meV from an ILE in a MoSe2/WSe2 heterostructure fabricated using state-of-the-art preparation techniques. These peaks have nearly equal intensity, indicating they are of common character, and have opposite circular polarizations when excited with circularly polarized light. Ab initio calculations successfully account for these observations: they show that both emission features originate from excitonic transitions that are indirect in momentum space and are split by spin-orbit coupling. Also, the electron is strongly hybridized between both the MoSe2 and WSe2 layers, with significant weight in both layers, contrary to the commonly assumed model. Thus, the transitions are not purely interlayer in character. This work represents a significant advance in our understanding of the static and dynamic properties of TMD heterostructures.


Journal Article
TL;DR: It is proposed that the presence of perpendicular crystalline mirror planes can protect three-dimensional band crossings characterized by nontrivial links such as a Hopf link or a coupled chain, giving rise to a variety of new types of topological semimetals.
Abstract: Topological semimetals can be classified by the connectivity and dimensionality of the band crossings in momentum space. The band crossings of a Dirac, Weyl, or an unconventional fermion semimetal are zero-dimensional (0D) points, whereas the band crossings of a nodal-line semimetal are one-dimensional (1D) closed loops. Here we propose that the presence of perpendicular crystalline mirror planes can protect three-dimensional (3D) band crossings characterized by nontrivial links such as a Hopf link or a coupled chain, giving rise to a variety of new types of topological semimetals. We show that the nontrivial winding number protects topological surface states distinct from those in previously known topological semimetals with a vanishing spin-orbit interaction. We also show that these nontrivial links can be engineered by tuning the mirror eigenvalues associated with the perpendicular mirror planes. Using first-principles band structure calculations, we predict the ferromagnetic full Heusler compound Co_{2}MnGa as a candidate. Both Hopf link and chainlike bulk band crossings and unconventional topological surface states are identified.


Journal Article
TL;DR: In this article, the authors model the unknown vector field using a deep neural network, imposing a Runge-Kutta integrator structure to isolate this vector field even when the data has a non-uniform timestep, thus constraining and focusing the modeling effort.
Abstract: A critical challenge in the data-driven modeling of dynamical systems is producing methods robust to measurement error, particularly when data is limited. Many leading methods either rely on denoising prior to learning or on access to large volumes of data to average over the effect of noise. We propose a novel paradigm for data-driven modeling that simultaneously learns the dynamics and estimates the measurement noise at each observation. By constraining our learning algorithm, our method explicitly accounts for measurement error in the map between observations, treating both the measurement error and the dynamics as unknowns to be identified, rather than assuming idealized noiseless trajectories. We model the unknown vector field using a deep neural network, imposing a Runge-Kutta integrator structure to isolate this vector field, even when the data has a non-uniform timestep, thus constraining and focusing the modeling effort. We demonstrate the ability of this framework to form predictive models on a variety of canonical test problems of increasing complexity and show that it is robust to substantial amounts of measurement error. We also discuss issues with the generalizability of neural network models for dynamical systems and provide open-source code for all examples.