Exact representations of many-body interactions with restricted-Boltzmann-machine neural networks

Adaptive autoencoder latent space tuning for more robust machine learning beyond the training set for six-dimensional phase space diagnostics of a time-varying ultrafast electron-diffraction compact accelerator

We present a general adaptive latent space tuning approach for improving the robustness of machine learning tools with respect to time variation and distribution shift. We demonstrate our approach by developing an encoder-decoder convolutional neural network-based virtual 6D phase space diagnostic of charged particle beams in the HiRES ultrafast electron diffraction (UED) compact particle accelerator with uncertainty quantification. Our method utilizes model-independent adaptive feedback to tune a low-dimensional 2D latent space representation of ∼1 million dimensional objects which are the 15 unique 2D projections (x,y),...,(z,p_{z}) of the 6D phase space (x,y,z,p_{x},p_{y},p_{z}) of the charged particle beams. We demonstrate our method with numerical studies of short electron bunches utilizing experimentally measured UED input beam distributions.

An adaptive approach to machine learning for compact particle accelerators

Machine learning (ML) tools are able to learn relationships between the inputs and outputs of large complex systems directly from data. However, for time-varying systems, the predictive capabilities of ML tools degrade if the systems are no longer accurately represented by the data with which the ML models were trained. For complex systems, re-training is only possible if the changes are slow relative to the rate at which large numbers of new input-output training data can be non-invasively recorded. In this work, we present an approach to deep learning for time-varying systems that does not require re-training, but uses instead an adaptive feedback in the architecture of deep convolutional neural networks (CNN). The feedback is based only on available system output measurements and is applied in the encoded low-dimensional dense layers of the encoder-decoder CNNs. First, we develop an inverse model of a complex accelerator system to map output beam measurements to input beam distributions, while both the accelerator components and the unknown input beam distribution vary rapidly with time. We then demonstrate our method on experimental measurements of the input and output beam distributions of the HiRES ultra-fast electron diffraction (UED) beam line at Lawrence Berkeley National Laboratory, and showcase its ability for automatic tracking of the time varying photocathode quantum efficiency map. Our method can be successfully used to aid both physics and ML-based surrogate online models to provide non-invasive beam diagnostics.

Neural-Network Quantum States for Spin-1 Systems: Spin-Basis and Parameterization Effects on Compactness of Representations

Neural network quantum states (NQS) have been widely applied to spin-1/2 systems, where they have proven to be highly effective. The application to systems with larger on-site dimension, such as spin-1 or bosonic systems, has been explored less and predominantly using spin-1/2 Restricted Boltzmann Machines (RBMs) with a one-hot/unary encoding. Here, we propose a more direct generalization of RBMs for spin-1 that retains the key properties of the standard spin-1/2 RBM, specifically trivial product states representations, labeling freedom for the visible variables and gauge equivalence to the tensor network formulation. To test this new approach, we present variational Monte Carlo (VMC) calculations for the spin-1 anti-ferromagnetic Heisenberg (AFH) model and benchmark it against the one-hot/unary encoded RBM demonstrating that it achieves the same accuracy with substantially fewer variational parameters. Furthermore, we investigate how the hidden unit complexity of NQS depend on the local single-spin basis used. Exploiting the tensor network version of our RBM we construct an analytic NQS representation of the Affleck-Kennedy-Lieb-Tasaki (AKLT) state in the xyz spin-1 basis using only M=2N hidden units, compared to M∼O(N2) required in the Sz basis. Additional VMC calculations provide strong evidence that the AKLT state in fact possesses an exact compact NQS representation in the xyz basis with only M=N hidden units. These insights help to further unravel how to most effectively adapt the NQS framework for more complex quantum systems.