Noise-aware Physics-informed Machine Learning for Robust PDE Discovery

This work is concerned with discovering the governing partial differential equation (PDE) of a physical system. Existing methods have demonstrated the PDE identification from finite observations but failed to maintain satisfying results against noisy data, partly owing to suboptimal estimated derivatives and found PDE coefficients. We address the issues by introducing a noise-aware physics-informed machine learning (nPIML) framework to discover the governing PDE from data following arbitrary distributions. We propose training a couple of neural networks, namely solver and preselector, in a multi-task learning paradigm, which yields important scores of basis candidates that constitute the hidden physical constraint. After they are jointly trained, the solver network estimates potential candidates, e.g., partial derivatives, for the sparse regression to initially unveil the most likely parsimonious PDE, decided according to information criterion. Denoising physics-informed neural networks (dPINNs), based on Discrete Fourier Transform (DFT), is proposed to deliver the optimal PDE coefficients respecting the noise-reduced variables. Extensive experiments on five canonical PDEs affirm that the proposed framework presents a robust and interpretable approach for PDE discovery, leading to a new automatic PDE selection algorithm established on minimization of the information criterion decay rate.

Multi-Kernel Temporal and Spatial Convolution for EEG-Based Emotion Classification

Deep learning using an end-to-end convolutional neural network (ConvNet) has been applied to several electroencephalography (EEG)-based brain-computer interface tasks to extract feature maps and classify the target output. However, the EEG analysis remains challenging since it requires consideration of various architectural design components that influence the representational ability of extracted features. This study proposes an EEG-based emotion classification model called the multi-kernel temporal and spatial convolution network (MultiT-S ConvNet). The multi-scale kernel is used in the model to learn various time resolutions, and separable convolutions are applied to find related spatial patterns. In addition, we enhanced both the temporal and spatial filters with a lightweight gating mechanism. To validate the performance and classification accuracy of MultiT-S ConvNet, we conduct subject-dependent and subject-independent experiments on EEG-based emotion datasets: DEAP and SEED. Compared with existing methods, MultiT-S ConvNet outperforms with higher accuracy results and a few trainable parameters. Moreover, the proposed multi-scale module in temporal filtering enables extracting a wide range of EEG representations, covering short- to long-wavelength components. This module could be further implemented in any model of EEG-based convolution networks, and its ability potentially improves the model's learning capacity.

Learning Subject-Generalized Topographical EEG Embeddings Using Deep Variational Autoencoders and Domain-Adversarial Regularization

Two of the biggest challenges in building models for detecting emotions from electroencephalography (EEG) devices are the relatively small amount of labeled samples and the strong variability of signal feature distributions between different subjects. In this study, we propose a context-generalized model that tackles the data constraints and subject variability simultaneously using a deep neural network architecture optimized for normally distributed subject-independent feature embeddings. Variational autoencoders (VAEs) at the input level allow the lower feature layers of the model to be trained on both labeled and unlabeled samples, maximizing the use of the limited data resources. Meanwhile, variational regularization encourages the model to learn Gaussian-distributed feature embeddings, resulting in robustness to small dataset imbalances. Subject-adversarial regularization applied to the bi-lateral features further enforces subject-independence on the final feature embedding used for emotion classification. The results from subject-independent performance experiments on the SEED and DEAP EEG-emotion datasets show that our model generalizes better across subjects than other state-of-the-art feature embeddings when paired with deep learning classifiers. Furthermore, qualitative analysis of the embedding space reveals that our proposed subject-invariant bi-lateral variational domain adversarial neural network (BiVDANN) architecture may improve the subject-independent performance by discovering normally distributed features.

Explainable and unexpectable recommendations using relational learning on multiple domains

In this research, we combine relational learning with multi-domain to develop a formal framework for a recommendation system. The design of our framework aims at: (i) constructing general rules for recommendations, (ii) providing suggested items with clear and understandable explanations, (iii) delivering a broad range of recommendations including novel and unexpected items. We use relational learning to find all possible relations, including novel relations, and to form the general rules for recommendations. Each rule is represented in relational logic, a formal language, associating with probability. The rules are used to suggest the items, in any domain, to the user whose preferences or other properties satisfy the conditions of the rule. The information described by the rule serves as an explanation for the suggested item. It states clearly why the items are chosen for the users. The explanation is in if-then logical format which is unambiguous, less redundant and more concise compared to a natural language used in other explanation recommendation systems. The explanation itself can help persuade the user to try out the suggested items, and the associated probability can drive the user to make a decision easier and faster with more confidence. Incorporating information or knowledge from multiple domains allows us to broaden our search space and provides us with more opportunities to discover items which are previously unseen or surprised to a user resulting in a wide range of recommendations. The experiment results show that our proposed algorithm is very promising. Although the quality of recommendations provided by our framework is moderate, our framework does produce interesting recommendations not found in the primitive single-domain based system and with simple and understandable explanations.

Correlation between mobility and the hydrogen bonding network of water at an electrified-graphite electrode using molecular dynamics simulation

Mobility and hydrogen bonding network of water at a graphite electrode: effects of dissolved ions and applied potential.

Attenuated total reflectance far-ultraviolet and deep-ultraviolet spectroscopy analysis of the electronic structure of a dicyanamide-based ionic liquid with Li+

Elucidating the unique electronic structure of ionic liquid molecules around Li⁺ using electronic absorption spectroscopy, theoretical calculations, and chemometric analyses.

Potential dependent changes in the structural and dynamical properties of 1-butyl-3-methylimidazolium bis(trifluoromethanesulfonyl)imide on graphite electrodes revealed by molecular dynamics simulations

Surface distributions and the dynamic properties of an ionic liquid on charged graphite electrodes.

Systematic analysis of various ionic liquids by attenuated total reflectance spectroscopy (145–450 nm) and quantum chemical calculations

Electronic absorption spectra in 140–450 nm were investigated by attenuated total reflectance spectroscopy and quantum chemical calculations.

Microscopic properties of ionic liquid/organic semiconductor interfaces revealed by molecular dynamics simulations

Structural and dynamic properties of an ionic liquid are compared on several organic semiconductors.

Statistical sleep pattern modelling for sleep quality assessment based on sound events

A good sleep is important for a healthy life. Recently, several consumer sleep devices have emerged on the market claiming that they can provide personal sleep monitoring; however, many of them require additional hardware or there is a lack of scientific evidence regarding their reliability. In this paper we proposed a novel method to assess the sleep quality through sound events recorded in the bedroom. We used subjective sleep quality as training label, combined several machine learning approaches including kernelized self organizing map, hierarchical clustering and hidden Markov model, obtained the models to indicate the sleep pattern of specific quality level. The proposed method is different from traditional sleep stage based method, provides a new aspect of sleep monitoring that sound events are directly correlated with the sleep of a person.

Structural Effects on the Incident Photon-to-Current Conversion Efficiency of Zn Porphyrin Dyes on the Low-Index Planes of TiO2

The structural effects of substrates on the incident photon-to-current conversion efficiency (IPCE) of Zn porphyrin (ZnP) dyes (ZnP-ref, YD2, and ZnPBAT) have been studied on well-defined single-crystal surfaces of rutile TiO₂ (TiO₂(111), TiO₂(100), and TiO₂(110)). IPCE of ZnP-ref depends on the structure of the substrates remarkably: TiO₂(100) < TiO₂(110) < TiO₂(111). IPCE of ZnP-ref/TiO₂(111) is 13 times as high as that of ZnP-ref/TiO₂(100) at 570 nm. YD2 and ZnPBAT also give the highest IPCE on TiO₂(111). The relative coverages of the porphyrin dyes give the following order: TiO₂(111) < TiO₂(110) < TiO₂(100). This order is opposite to that of IPCEs. The orientation of the dyes is predicted using density functional theory calculations on simplified models of TiO₂ surfaces. The highest IPCE on TiO₂(111) is attributed to the high rate of electron transfer through the space due to the fluctuation of the tilt angle of the adsorbed dyes.

A relationship between the force curve measured by atomic force microscopy in an ionic liquid and its density distribution on a substrate

A relationship between the force curve measured in an ionic liquid and the solvation structure is studied. Applying the obtained relationship, candidates of the solvation structure are estimated from a measured force curve.

Potential-dependent structures investigated at the perchloric acid solution/iodine modified Au(111) interface by electrochemical frequency-modulation atomic force microscopy

Highly sensitive force measurements revealed that hydration and geometrical structures at the iodine terminated Au(111) surface were reversibly modified by applying electrode potentials.

Molecularly clean ionic liquid/rubrene single-crystal interfaces revealed by frequency modulation atomic force microscopy

Frequency modulation atomic force microscopy was employed to show a molecularly clean interface between an ionic liquid and a rubrene single crystal for possible applications to electric double-layer field-effect transistors.

First direct visualization of spillover species emitted from pt nanoparticles

We studied the methanol adsorption behavior of Pt nanoparticles that were vacuum-deposited on a TiO(2)(110) surface at room temperature by using an ultrahigh vacuum (UHV) scanning tunneling microscope (STM). A large number of bright spots were observed on fivefold-coordinated Ti (Ti(5c)) rows of the TiO(2)(110) surface after exposure of the Pt/TiO(2)(110) to methanol vapor. We assigned the bright spots to methoxy species. These were mobile and were found to hop along the Ti(5c) rows. In situ time-resolved STM observations of the formation and migration of the bright spots on the Pt/TiO(2)(110) were carried out in the presence of methanol. The bright spots were produced at the periphery of the Pt nanoparticles and migrated to the substrate Ti(5c) rows. We discuss the spillover process and behavior of the methoxy species on the Pt/TiO(2)(110).

Direct observation of layered structures at ionic liquid/solid interfaces by using frequency-modulation atomic force microscopy

Presence of inhomogeneous layered structures of ionic liquid (IL) molecules at IL/HOPG and IL/mica interfaces was directly detected and imaged by using frequency-modulation atomic force microscopy. High stability of the layered structures may disturb their interface applications to catalysis and electrochemistry.

Photoswitching tripodal single molecular tip for noncontact AFM measurements: synthesis, immobilization, and reversible configurational change on gold surface

Tripodal molecules consisting of a tetrasubstituted adamantane with three phenylacetylene legs and a reversibly photoswitching apex were designed as "single molecular tips" for both chemical and topographical characterization of the substrate surface. By covalent attachment onto gold-coated AFM tips through three S-Au bonds, these rigid tripodal molecules are expected to act as sharp, robust, and stationary molecular tips whose configuration can be reversibly changed upon irradiation with UV or visible light. In this report, the full account of the syntheses of two photoswitching tripodal molecular tips, their immobilization onto Au(111) surfaces, and the detection of photoinduced configurational change on Au(111) surface by SPM measurements are documented.

Observation of redox-state-dependent reversible local structural change of ferrocenyl-terminated molecular island by electrochemical frequency modulation AFM

Electroactive ferrocenylundecanethiol (FcC(11)H(22)SH) islands embedded in an n-decanethiol (C(10)H(21)SH) self-assembled monolayer (SAM) matrix on Au(111) were studied under potential control in 0.1 M HClO(4) aqueous solution using newly developed electrochemical frequency-modulation atomic force microscopy (EC-FM-AFM). The apparent height of the Fc islands from the surface of the matrix SAM increased by about 0.44 nm accompanied by the oxidation of the terminal Fc groups. This potential-dependent reversible change can be explained by formation of an ionic double layer where ClO(4)(-) ions are strongly bound on the Fc(+) groups. Simultaneous measurements of energy dissipation, which corresponds to the energy to keep the cantilever's vibrational amplitude constant, revealed distinct change in the magnitude by the oxidation state of the Fc groups. These results indicate that localized charge at an electrode/electrolyte solution interface can be identified, and microscopic information on the electric double layer at the interface is available by using EC-FM-AFM.

Strong Intermolecular Electronic Coupling within a Tetrathiafulvalene Island Embedded in Self-Assembled Monolayers

Electroactive tetrathiafulvalene thiol, specially designed to pursue an intermolecular electronic coupling, was embedded in an n-alkanethiol SAM matrix as islands and was studied under potential control using in situ scanning tunneling microscopy. The apparent height of the islands increased with the island size, irrespective of the oxidation state of the tetrathiafulvalene backbones. This behavior can be rationalized on the basis of the strong intermolecular electronic coupling that creates efficient intermolecular conduction paths.

Dynamic and Collective Electrochemical Responses of Tetrathiafulvalene Derivative Self-Assembled Monolayers

Electroactive tetrathiafulvalene (TTF)-containing alkanethiol self-assembled monolayers (SAMs) were designed and synthesized to elucidate the relationship between electrochemical responses and film structures. Two TTF derivative molecules having one alkanethiol chain (1) and two alkanethiol chains (2) were utilized to modulate the molecular packing arrangements in the SAMs, and the formation and structure of the SAMs were characterized by surface plasmon resonance spectroscopy (SPR). SPR measurements in various contacting media demonstrated loose packing of SAM 1 and close packing of SAM 2 due to the different space fillings of the molecules. Two successive one-electron redox waves were observed for both SAMs by cyclic voltammetry. The peak widths of the redox waves were strongly dependent on the oxidation states of the TTF moieties, the packing arrangement of the SAMs, and the contacting medium. We found that TTF-based SAMs exhibited collective electrochemical responses induced by dynamic structural changes, depending on the degree of freedom for the component molecules in the SAMs. These results imply that the molecular design, taking into account the electrochemical responses, extends the available range of molecular-based functionalities in TTF-based SAMs.

Magnetic and Electronic Properties of Palladium Nanoparticles Coated with π-Conjugated Tetrathiafulvalenes Derivative

Magnetic and electronic properties are investigated for Pd nanoparticles coated with a TTF-derivative (EDT-TTF(SCH(3))(SC(10)H(20)SH)) and octadecanethiol organic mixed monolayer. The temperature-independent spin susceptibility and spin concentration of Pd decrease upon the increasing proportion of the TTF-derivative in the organic layer. With the introduction of the derivative, the ESR broad signal originating from the interior of the Pd nanoparticles tends to vanish following the appearance of sharp signals due to the TTF radical. The presence of the TTF molecules enhances the charge transfer from the core Pd nanoparticles. The electronic state of the Pd nanoparticles changes as a consequence of the contributions of both the quantum-size effect and the charge-transfer effect between the Pd core, TTF-derivative, and alkanethiol.

Formation of One-Dimensional C60 Rows on TiO2(110)-1 × 2-cross-link Structure and Their Local Polymerization

Adsorption and growth of a C(60) monolayer on a TiO(2)(110)-1 x 2-cross-link structure were investigated by scanning tunneling microscopy (STM). Single C(60) molecules were preferentially anchored at the cross-link site due to interaction with undercoordinated Ti cations, and C(60) rows grew along the troughs between the 1 x 2-added rows. The C(60) monolayer structure is characterized by closely packed (r(C(60)-C(60)) = 1.0 nm) C(60) rows that are paired with every second added row (separation of paired rows is 1.1 nm). By applying a high negative bias voltage (-3.5 V) to an STM tip on the C(60) monolayer, C(60) oligomers were formed accompanied with the contraction of C(60)-C(60) distance along the C(60) row and bright contrast in the STM image.

Synthesis of Tris(tetrathiafulvaleno)dodecadehydro- [18]annulenes and Their Self-Assembly

[reaction: see text] Synthesis of electroactive tris(tetrathiafulvaleno)dodecadehydro[18]annulenes with ester substituents has been carried out with palladium-mediated cyclotrimerization of 4,5-diethynyl-TTFs. The TTF[18]annulenes produce stacked dimmers in solution and exhibit solvatochromism and thermochromism. The TTF[18]annulene-hexabutyl ester forms a molecular wire from an aqueous THF solution with cooperative S-S and pi-pi stacking interactions.

Photoswitching Behavior of a Novel Single Molecular Tip for Noncontact Atomic Force Microscopy Designed for Chemical Identification

A tripod molecule with an azobenzene arm was designed as a single molecular tip for noncontact atomic force microscopy (NC-AFM). The azobenzene moiety showed photoisomerization that enabled measurements of the same position of the sample by different tip apexes with different interactions. Photoswitching behavior of the molecule synthesized and adsorbed on Au surfaces was examined and reversible switching between the trans- and cis forms was successfully confirmed by NC-AFM measurements.

In Situ STM Study of Potential-Dependent Height Change of a Tetrathiafulvalene Derivative Embedded in Alkanethiol Self-Assembled Monolayers on Au(111)

Electroactive tetrathiafulvalene thiol islands embedded in an n-alkanethiol SAM matrix were studied under potential control using in situ scanning tunneling microscopy. Unlike previously studied stochastic switching, the apparent height of the island could be intentionally controlled in the present system by choosing the appropriate potential and the island size. The dependence of the height change on the potential and the size is explained as structural change of the island induced by the charging effect of the electroactive moiety.

Self-limiting growth of Pt nanoparticles from MeCpPtMe3 adsorbed on TiO2110 studied by scanning tunneling microscopy

The growth of Pt nanoparticles from the metal-organic precursor [MeCpPtMe3: (methylcyclopentadienyl) trimethyl platinum] on TiO2(110) was studied by scanning tunneling microscopy. 2D-like Pt particles on the surface were formed in a self-limiting growth mode. The inner structure of the particles was resolved as unique tetramerlike bright spots. A mechanism for the self-limiting growth of Pt particles is proposed.