The almost paradoxical concept of deterministic chaos describes systems which are so sensitive to initial conditions that long term forecasting becomes impossible. Therefore, despite the fact that there is no randomness in the dynamical equations, even the slightest error in calculation -- for instance numerical precision errors in a computer -- will cause future predictions to be wildly off. Applications of chaotic systems range from weather prediction, turbulent flows in fluids, plasma dynamics, chemical reactions, population dynamics, the motion of celestial bodies, the stock market, and many others. While current techniques tend to use noisy and partial measurement information to constrain a physical model (https://en.wikipedia.org/wiki/Kalman_filter), Therefore it is important to be able to use data driven methods such as machine learning (ML) to forecast such systems.

The Dynamic Mode Decomposition has proved to be a very efficient technique to study dynamic data. This is entirely a data-driven approach that extracts all necessary information from data snapshots which are commonly supposed to be sampled from measurement. The application of this approach becomes problematic if the available data is incomplete because some dimensions of smaller scale either missing or unmeasured. Such setting occurs very often in modeling complex dynamical systems such as power grids, in particular with reduced-order modeling. To take into account the effect of unresolved variables the optimal prediction approach based on the Mori-Zwanzig formalism can be applied to obtain the most expected prediction under existing uncertainties. This effectively leads to the development of a time-predictive model accounting for the impact of missing data. In the present paper we provide a detailed derivation of the considered method from the Liouville equation and finalize it with the optimization problem that defines the optimal transition operator corresponding to the observed data. In contrast to the existing approach, we consider a first-order approximation of the Mori-Zwanzig decomposition, state the corresponding optimization problem and solve it with the gradient-based optimization method. The gradient of the obtained objective function is computed precisely through the automatic differentiation technique. The numerical experiments illustrate that the considered approach gives practically the same dynamics as the exact Mori-Zwanzig decomposition, but is less computationally intensive.

Quantum Annealing (QA) was originally intended for accelerating the solution of combinatorial optimization tasks that have natural encodings as Ising models. However, recent experiments on QA hardware platforms have demonstrated that, in the operating regime corresponding to weak interactions, the QA hardware behaves like a noisy Gibbs sampler at a hardware-specific effective temperature. This work builds on those insights and identifies a class of small hardware-native Ising models that are robust to noise effects and proposes a procedure for executing these models on QA hardware to maximize Gibbs sampling performance. Experimental results indicate that the proposed protocol results in high-quality Gibbs samples from a hardware-specific effective temperature. Furthermore, we show that this effective temperature can be adjusted by modulating the annealing time and energy scale. The procedure proposed in this work provides an approach to using QA hardware for Ising model sampling presenting potential new opportunities for applications in machine learning and physics simulation.

Reliably and physically accurately transferring information between images through deformable image registration with large anatomical differences is an open challenge in medical image analysis. Most existing methods have two key shortcomings: first, they require extensive up-front parameter tuning to each specific registration problem, and second, they have difficulty capturing large deformations and content mismatches between images. There have however been developments that have laid the foundation for potential solutions to both shortcomings. Towards the first shortcoming, a multi-objective optimization approach using the Real-Valued Gene-pool Optimal Mixing Evolutionary Algorithm (RV-GOMEA) has been shown to be capable of producing a diverse set of registrations for 2D images in one run of the algorithm, representing different trade-offs between conflicting objectives in the registration problem. This allows the user to select a registration afterwards and removes the need for up-front tuning. Towards the second shortcoming, a dual-dynamic grid transformation model has proven effective at capturing large differences in 2D images. These two developments have recently been accelerated through GPU parallelization, delivering large speed-ups. Based on this accelerated version, it is now possible to extend the approach to 3D images. Concordantly, this work introduces the first method for multi-objective 3D deformable image registration, using a 3D dual-dynamic grid transformation model based on simplex meshes while still supporting the incorporation of annotated guidance information and multi-resolution schemes. Our proof-of-concept prototype shows promising results on synthetic and clinical 3D registration problems, forming the foundation for a new, insightful method that can include bio-mechanical properties in the registration.

Energy disaggregation, known in the literature as Non-Intrusive Load Monitoring (NILM), is the task of inferring the energy consumption of each appliance given the aggregate signal recorded by a single smart meter. In this paper, we propose a novel two-stage optimization-based approach for energy disaggregation. In the first phase, a small training set consisting of disaggregated power profiles is used to estimate the parameters and the power states by solving a mixed integer programming problem. Once the model parameters are estimated, the energy disaggregation problem is formulated as a constrained binary quadratic optimization problem. We incorporate penalty terms that exploit prior knowledge on how the disaggregated traces are generated, and appliance-specific constraints characterizing the signature of different types of appliances operating simultaneously. Our approach is compared with existing optimization-based algorithms both on a synthetic dataset and on three real-world datasets. The proposed formulation is computationally efficient, able to disambiguate loads with similar consumption patterns, and successfully reconstruct the signatures of known appliances despite the presence of unmetered devices, thus overcoming the main drawbacks of the optimization-based methods available in the literature.

We propose an extended generalization of the pseudo Huber loss formulation. We show that using the log-exp transform together with the logistic function, we can create a loss which combines the desirable properties of the strictly convex losses with robust loss functions. With this formulation, we show that a linear convergence algorithm can be utilized to find a minimizer. We further discuss the creation of a quasi-convex composite loss and provide a derivative-free exponential convergence rate algorithm.

Mathematical optimization (MO) technologies are being utilized today by leading global companies across industries – including aviation, energy, finance, logistics, telecommunications, manufacturing, media, and many more – to solve a wide range of complex, real-world problems, make optimal, data-driven decisions, and achieve greater operational efficiency. An increasing number of data scientists are adding MO into their analytics toolbox and developing applications that combine MO and machine learning (ML) technologies. In this series of webinars, we will show you how – with MO techniques – you can build interpretable models to tackle your prediction and classification problems. How to formulate an MO model. How to build an MO model using the Gurobi Python API.

From simulating new and more efficient materials to predicting how the stock market will change with greater precision, the ramifications of quantum computing for businesses are potentially huge. The world's biggest companies are now launching quantum computing programs, and governments are pouring money into quantum research. For systems that have yet prove useful, quantum computers are certainly garnering lots of attention. Quantum computers offer great promise for cryptography and optimization problems, and companies are racing to make them practical for business use. ZDNet explores what quantum computers will and won't be able to do, and the challenges that remain.

Evolutionary strategies have recently been shown to achieve competing levels of performance for complex optimization problems in reinforcement learning. In such problems, one often needs to optimize an objective function subject to a set of constraints, including for instance constraints on the entropy of a policy or to restrict the possible set of actions or states accessible to an agent. Convergence guarantees for evolutionary strategies to optimize stochastic constrained problems are however lacking in the literature. In this work, we address this problem by designing a novel optimization algorithm with a sufficient decrease mechanism that ensures convergence and that is based only on estimates of the functions. We demonstrate the applicability of this algorithm on two types of experiments: i) a control task for maximizing rewards and ii) maximizing rewards subject to a non-relaxable set of constraints.

Sequential model-based optimization sequentially selects a candidate point by constructing a surrogate model with the history of evaluations, to solve a black-box optimization problem. Gaussian process (GP) regression is a popular choice as a surrogate model, because of its capability of calculating prediction uncertainty analytically. On the other hand, an ensemble of randomized trees is another option and has practical merits over GPs due to its scalability and easiness of handling continuous/discrete mixed variables. In this paper we revisit various ensembles of randomized trees to investigate their behavior in the perspective of prediction uncertainty estimation. Then, we propose a new way of constructing an ensemble of randomized trees, referred to as BwO forest, where bagging with oversampling is employed to construct bootstrapped samples that are used to build randomized trees with random splitting. Experimental results demonstrate the validity and good performance of BwO forest over existing tree-based models in various circumstances.