Ordinary differential equations (ODEs) are a widely used formalism for the mathematical modeling of dynamical systems, a task omnipresent in scientific domains. The paper introduces a novel method for inferring ODEs from data, which extends ProGED, a method for equation discovery that allows users to formalize domain-specific knowledge as probabilistic context-free grammars and use it for constraining the space of candidate equations. The extended method can discover ODEs from partial observations of dynamical systems, where only a subset of state variables can be observed. To evaluate the performance of the newly proposed method, we perform a systematic empirical comparison with alternative state-of-the-art methods for equation discovery and system identification from complete and partial observations. The comparison uses Dynobench, a set of ten dynamical systems that extends the standard Strogatz benchmark. We compare the ability of the considered methods to reconstruct the known ODEs from synthetic data simulated at different temporal resolutions. We also consider data with different levels of noise, i.e., signal-to-noise ratios. The improved ProGED compares favourably to state-of-the-art methods for inferring ODEs from data regarding reconstruction abilities and robustness to data coarseness, noise, and completeness.

Equation discovery, also known as symbolic regression, is a machine learning task of inducing closed-form equations from data and background knowledge. The latter takes various forms. Domain-specific knowledge can constrain the space of candidate equations to those that make sense in the scientific or engineering domain of use. Cross-domain knowledge, on the other hand, imposes general rules for model acceptability, such as parsimony, understandability, or consistency of the equations with the dimensional units of the variables. In this paper, we propose using attribute grammars to ensure the induced equations' dimensional consistency. Attribute grammars are flexible enough to combine cross-domain knowledge on dimensional consistency with domain-specific knowledge expressed as a probabilistic context-free grammar. At the same time, we show that attribute grammars can be efficiently transformed into probabilistic context-free grammars for equation discovery with existing algorithms. Finally, we provide empirical evidence that attribute grammars ensuring dimensional consistency of equations can significantly improve the performance of equation discovery on the standard set of a hundred Feynman benchmarks.

Noisy intermediate-scale quantum (NISQ) devices are spearheading the second quantum revolution. Of these, quantum annealers are the only ones currently offering real world, commercial applications on as many as 5000 qubits. The size of problems that can be solved by quantum annealers is limited mainly by errors caused by environmental noise and intrinsic imperfections of the processor. We address the issue of intrinsic imperfections with a novel error correction approach, based on machine learning methods. Our approach adjusts the input Hamiltonian to maximize the probability of finding the solution. In our experiments, the proposed error correction method improved the performance of annealing by up to three orders of magnitude and enabled the solving of a previously intractable, maximally complex problem.

The dynobench repository contains a benchmark for system identification methods. Currently includes models of 10 dynamical systems: Bacterial respiration, Bar magnets, Glider, Lotka-Volterra, Predator-Prey, Shearflow and Van der Pol from the Strogatz dataset, as well as Lorenz, Coupled phase oscillators and Stuart-Landau models for dynamical systems that often appear in the research community. They also add variety to the benchmark as the Lorenz oscillator model introduces a larger set of state variables (three compared to two), and the coupled phase oscillators model is non-autonomous, which is reflected in the explicit incorporation of time in its equations. The repository contains the 'data' folder, where the simulations of ten dynamical systems are stored, simulated under 6 different configurations of data quality. The first dimention modifies the data length and coarseness, where a 'small' dataset includes simulations of 10 seconds with a 0.1 sampling step, and a 'large' dataset includes simulations of 20 seconds with a 0.01 sampling step. The second dimention of data quality modifies the amount of noise in the data, where there are three levels of noise (no noise, moderate levels with 30 dB signal-to-noise ratio and high levels of noise with 13 dB signal-to-noise ratio). The data can be used by itself, without the need to look at the python code. The repository also contains the main.py script by which the data can be generated. The 'src' folder contains additional python scripts that are needed to generate the data. The data were created by first randomly setting the initial values for one category, in particular a configuration of 'small', 'noise-free' and 'train' data (using inits_type = "random"). Then, all the other configurations were generated by using the same initial values. Inside the script main.py there is more information about the settings and how to run the script. The benchmark was created as a part of the research described in the paper titled Probabilistic grammars for modeling dynamical systems from coarse, noisy, and partial data, written by Omejc et al. (in submission).

Inversion of radiative transfer models (RTMs) is key to interpreting satellite observations of air quality and greenhouse gases, but is computationally expensive. Surrogate models that emulate the full forward physical RTM can speed up the simulation, reducing computational and timing costs and allowing the use of more advanced physics for trace gas retrievals. In this study, we present the development of surrogate models for two RTMs: the RemoTeC algorithm using the LINTRAN RTM and the SCIATRAN RTM. We estimate the intrinsic dimensionality of the input and output spaces and embed them in lower dimensional subspaces to facilitate the learning task. Two methods are tested for dimensionality reduction, autoencoders and principle component analysis (PCA), with PCA consistently outperforming autoencoders. Different sampling methods are employed for generating the training datasets: sampling focused on expected atmospheric parameters and latin hypercube sampling. The results show that models trained on the smaller (n = 1000) uniformly sampled dataset can perform as well as those trained on the larger (n = 50000), more focused dataset. Surrogate models for both datasets are able to accurately emulate Sentinel 5P spectra within a millisecond or less, as compared to the minutes or hours needed to simulate the full physical model. The SCIATRAN-trained forward surrogate models are able to generalize the emulation to a broader set of parameters and can be used for less constrained applications, while achieving a normalized RMSE of 7.3%. On the other hand, models trained on the LINTRAN dataset can completely replace the RTM simulation in more focused expected ranges of atmospheric parameters, as they achieve a normalized RMSE of 0.3%.

Ordinary differential equations (ODEs) are a widely used formalism for mathematical modeling of dynamical systems, a task omnipresent in many scientific domains. The paper introduces a novel method for inferring ODEs from data. It extends ProGED, a method for equation discovery that employs probabilistic context-free grammars for constraining the space of candidate equations. The proposed method can discover ODEs from partial observations of dynamical systems, where only a subset of state variables can be observed. The new method's empirical evaluation shows it can reconstruct the ODEs of the well-known Van der Pol oscillator from synthetic simulation data. In terms of reconstruction performance, improved ProGED compares favorably to state-of-the-art methods for inferring ODEs from data.

The added value of supervised Machine Learning (ML) methods to determine the Absolute Configuration (AC) of compounds from their Vibrational Circular Dichroism (VCD) spectra was explored. Among all ML methods considered, Random Forest (RF) and Feedforward Neural Network (FNN) yield the best performance for identification of the AC. At its best, FNN allows near-perfect AC determination, with accuracy of prediction up to 0.995, while RF combines good predictive accuracy (up to 0.940) with the ability to identify the spectral areas important for the identification of the AC. No loss in performance of either model is observed as long as the spectral sampling interval used does not exceed the spectral bandwidth. Increasing the sampling interval proves to be the best method to lower the dimensionality of the input data, thereby decreasing the computational cost associated with the training of the models.

Surrogate models approximate the predictions of other models. The motivation for learning surrogate models can come from computational concerns, when the predictions of the original model are computationally expensive to obtain. In contrast, the surrogate models are computationally efficient. In this paper, we propose a framework for machine learning of surrogate models, which operate on the same input and output spaces as their original models. Instead of learning direct mappings from the input to the output space (and vice versa), we first assess the intrinsic dimensionality of the input and output spaces and reduce it appropriately, by using PCA and autoencoders. Predictive models are learned on the reduced spaces by the use of neural networks and their predictions are mapped to the original spaces. We apply the framework to learn a surrogate model for a complex radiative transfer model RemoTeC, designed and built at SRON in the Netherlands. The original model predicts shortwave infrared (SWIR) spectra, for a given state vector of atmospheric parameters, representative of any geo-location that the Sentinel 5P satellite may encounter. The results indicate a low dimensionality of both the input and the output space and are accurate in both the forward and reverse direction.

A comparative experimental investigation of the dependence of second harmonic generation (SHG) on applied external voltage between the standard nematic liquid crystalline material and an analogue ferromagnetic nematic liquid crystalline material was performed by using a fundamental optical beam at 800 nm wavelength. For a ferromagnetic material, the dependence of SHG on an applied magnetic field was also examined. Three different polarization combinations of the fundamental and the second harmonic radiation were analysed. The SHG signal observed in the former material is attributed to a combination of electric field-induced SHG (EFISHG) and flexoelectric deformation-induced SHG, while SHG signal observed in the latter material is attributed solely to flexoelectric deformation-induced SHG. The obtained dependences of the SHG signal on the associated optical retardation show that in the most favourable polarization combination the two contributions generate about the same effective nonlinear optical susceptibility.

A study of bright matter-wave solitons of a cesium Bose-Einstein condensate (BEC) is presented. Production of a single soliton is demonstrated and dependence of soliton atom number on the interatomic interaction is investigated. Formation of soliton trains in the quasi-one-dimensional confinement is shown. Additionally, fragmentation of a BEC has been observed outside confinement, in free space. In the end a double BEC production setup for studying soliton collisions is described.