Gradient-augmented supervised learning of optimal feedback laws using state-dependent Riccati equations

A supervised learning approach for the solution of large-scale nonlinear stabilization problems is presented. A stabilizing feedback law is trained from a dataset generated from State-dependent Riccati Equation solvers. The training phase is enriched by the use of gradient information in the loss function, which is weighted through the use of hyperparameters. High-dimensional nonlinear stabilization tests demonstrate that real-time sequential large-scale Algebraic Riccati Equation solvers can be substituted by a suitably trained feedforward neural network

How Important is Weight Symmetry in Backpropagation?

Gradient backpropagation (BP) requires symmetric feedforward and feedback connections—the same weights must be used for forward and backward passes. This “weight transport problem” [1] is thought to be one of the main reasons of BP’s biological implausibility. Using 15 different classification datasets, we systematically study to what extent BP really depends on weight symmetry. In a study that turned out to be surprisingly similar in spirit to Lillicrap et al.’s demonstration [2] but orthogonal in its results, our experiments indicate that: (1) the magnitudes of feedback weights do not matter to performance (2) the signs of feedback weights do matter—the more concordant signs between feedforward and their corresponding feedback connections, the better (3) with feedback weights having random magnitudes and 100% concordant signs, we were able to achieve the same or even better performance than SGD. (4) some normalizations/stabilizations are indispensable for such asymmetric BP to work, namely Batch Normalization (BN) [3] and/or a “Batch Manhattan” (BM) update rule.This work was supported by the Center for Brains, Minds and Machines (CBMM), funded by NSF STC award CCF - 1231216

How important is weight symmetry in backpropagation?

Gradient backpropagation (BP) requires symmetric feedforward and feedback connections-the same weights must be used for forward and backward passes. This "weight transport problem" (Grossberg 1987) is thought to be one of the main reasons to doubt BP's biologically plausibility. Using 15 different classification datasets, we systematically investigate to what extent BP really depends on weight symmetry. In a study that turned out to be surprisingly similar in spirit to Lillicrap et al.'s demonstration (Lillicrap et al. 2014) but orthogonal in its results, our experiments indicate that: (1) the magnitudes of feedback weights do not matter to performance (2) the signs of feedback weights do matter-the more concordant signs between feedforward and their corresponding feedback connections, the better (3) with feedback weights having random magnitudes and 100% concordant signs, we were able to achieve the same or even better performance than SGD. (4) some normalizations/stabilizations are indispensable for such asymmetric BP to work, namely Batch Normalization (BN) (Ioffe and Szegedy 2015) and/or a "Batch Manhattan" (BM) update rule.National Science Foundation (U.S.) (STC Award CCF 1231216

Modelling and control of chaotic processes through their Bifurcation Diagrams generated with the help of Recurrent Neural Network models: Part 1—simulation studies

Many real-world processes tend to be chaotic and also do not lead to satisfactory analytical modelling. It has been shown here that for such chaotic processes represented through short chaotic noisy time-series, a multi-input and multi-output recurrent neural networks model can be built which is capable of capturing the process trends and predicting the future values from any given starting condition. It is further shown that this capability can be achieved by the Recurrent Neural Network model when it is trained to very low value of mean squared error. Such a model can then be used for constructing the Bifurcation Diagram of the process leading to determination of desirable operating conditions. Further, this multi-input and multi-output model makes the process accessible for control using open-loop/closed-loop approaches or bifurcation control etc. All these studies have been carried out using a low dimensional discrete chaotic system of Hénon Map as a representative of some real-world processes

Demonstration of Machine Learning-Based Model-Independent Stabilization of Source Properties in Synchrotron Light Sources.

Synchrotron light sources, arguably among the most powerful tools of modern scientific discovery, are presently undergoing a major transformation to provide orders of magnitude higher brightness and transverse coherence enabling the most demanding experiments. In these experiments, overall source stability will soon be limited by achievable levels of electron beam size stability, presently on the order of several microns, which is still 1-2 orders of magnitude larger than already demonstrated stability of source position and current. Until now source size stabilization has been achieved through corrections based on a combination of static predetermined physics models and lengthy calibration measurements, periodically repeated to counteract drift in the accelerator and instrumentation. We now demonstrate for the first time how the application of machine learning allows for a physics- and model-independent stabilization of source size relying only on previously existing instrumentation. Such feed-forward correction based on a neural network that can be continuously online retrained achieves source size stability as low as 0.2  μm (0.4%) rms, which results in overall source stability approaching the subpercent noise floor of the most sensitive experiments

Design and optimization of Artificial Neural Networks for the modelling of superconducting magnets operation in tokamak fusion reactors

In superconducting tokamaks, the cryoplant provides the helium needed to cool different clients, among which by far the most important one is the superconducting magnet system. The evaluation of the transient heat load from the magnets to the cryoplant is fundamental for the design of the latter and the assessment of suitable strategies to smooth the heat load pulses, induced by the intrinsically pulsed plasma scenarios characteristic of today's tokamaks, is crucial for both suitable sizing and stable operation of the cryoplant. For that evaluation, accurate but expensive system-level models, as implemented in e.g. the validated state-of-the-art 4C code, were developed in the past, including both the magnets and the respective external cryogenic cooling circuits. Here we show how these models can be successfully substituted with cheaper ones, where the magnets are described by suitably trained Artificial Neural Networks (ANNs) for the evaluation of the heat load to the cryoplant. First, two simplified thermal-hydraulic models for an ITER Toroidal Field (TF) magnet and for the ITER Central Solenoid (CS) are developed, based on ANNs, and a detailed analysis of the chosen networks' topology and parameters is presented and discussed. The ANNs are then inserted into the 4C model of the ITER TF and CS cooling circuits, which also includes active controls to achieve a smoothing of the variation of the heat load to the cryoplant. The training of the ANNs is achieved using the results of full 4C simulations (including detailed models of the magnets) for conventional sigmoid-like waveforms of the drivers and the predictive capabilities of the ANN-based models in the case of actual ITER operating scenarios are demonstrated by comparison with the results of full 4C runs, both with and without active smoothing, in terms of both accuracy and computational time. Exploiting the low computational effort requested by the ANN-based models, a demonstrative optimization study has been finally carried out, with the aim of choosing among different smoothing strategies for the standard ITER plasma operation

Trajectories of land surface evolution in polygonal tundra

In the past three decades, an abrupt acceleration in the thaw of ice wedges has spurred rapid surface deformation (i.e., thermokarst) in polygonal tundra landscapes spanning the Arctic. The ensuing conversion of low-centered polygons (LCPs) and flat terrain into high-centered polygons (HCPs) has profound impacts on regional hydrology and carbon fluxes between the soil and atmosphere. However, pathways of ice wedge degradation and the stability of the deformed terrain are uncertain, complicating efforts to project feedbacks on global climate change. In this dissertation, I explore trajectories of surface deformation in ice wedge polygons, using a combination of calibration-constrained numerical experiments, remote sensing, and machine learning. In the first two chapters, numerical simulations of the soil hydrologic and thermal regimes reveal that, relative to terrain unaffected by thermokarst, the permafrost beneath HCPs tends to be well-buffered against climate extremes, promoting landscape stability. Ice wedges at HCP boundaries are less vulnerable to thaw during warm summers, reinforcing prior field-based observations that thermokarst is typically a self-arresting process. Simultaneously, the cooling of thermokarst-affected ice wedges in winter tends to be inhibited by snow accumulation in degraded troughs, reducing the likelihood of renewed ice wedge cracking and restoration of LCP microtopography. Overall, these results indicate that the microtopography of polygons already affected by thermokarst will likely remain stable over the next century. In the second half of this dissertation, a novel machine-learning-based tool is introduced for delineating and measuring the microtopography associated with ice wedge polygons in high-resolution digital elevation models. The tool is used to map polygonal geomorphology across ~1,000 km² of tundra south of Prudhoe Bay, Alaska, visualizing in unprecedented detail the heterogeneous extent to which thermokarst has affected a modern polygonal landscape. This map of polygonal geomorphology provides useful context for upscaling point- to plot-scale observations of gas exchange in ice wedge polygons to landscape-scale estimates of carbon fluxes. It also provides an extensive baseline dataset for quantifying contemporary rates of land surface deformation, through future surveys at the site.Geological Science