105,934 research outputs found
Learning deep dynamical models from image pixels
Modeling dynamical systems is important in many disciplines, e.g., control,
robotics, or neurotechnology. Commonly the state of these systems is not
directly observed, but only available through noisy and potentially
high-dimensional observations. In these cases, system identification, i.e.,
finding the measurement mapping and the transition mapping (system dynamics) in
latent space can be challenging. For linear system dynamics and measurement
mappings efficient solutions for system identification are available. However,
in practical applications, the linearity assumptions does not hold, requiring
non-linear system identification techniques. If additionally the observations
are high-dimensional (e.g., images), non-linear system identification is
inherently hard. To address the problem of non-linear system identification
from high-dimensional observations, we combine recent advances in deep learning
and system identification. In particular, we jointly learn a low-dimensional
embedding of the observation by means of deep auto-encoders and a predictive
transition model in this low-dimensional space. We demonstrate that our model
enables learning good predictive models of dynamical systems from pixel
information only.Comment: 10 pages, 11 figure
Data-driven discovery of coordinates and governing equations
The discovery of governing equations from scientific data has the potential
to transform data-rich fields that lack well-characterized quantitative
descriptions. Advances in sparse regression are currently enabling the
tractable identification of both the structure and parameters of a nonlinear
dynamical system from data. The resulting models have the fewest terms
necessary to describe the dynamics, balancing model complexity with descriptive
ability, and thus promoting interpretability and generalizability. This
provides an algorithmic approach to Occam's razor for model discovery. However,
this approach fundamentally relies on an effective coordinate system in which
the dynamics have a simple representation. In this work, we design a custom
autoencoder to discover a coordinate transformation into a reduced space where
the dynamics may be sparsely represented. Thus, we simultaneously learn the
governing equations and the associated coordinate system. We demonstrate this
approach on several example high-dimensional dynamical systems with
low-dimensional behavior. The resulting modeling framework combines the
strengths of deep neural networks for flexible representation and sparse
identification of nonlinear dynamics (SINDy) for parsimonious models. It is the
first method of its kind to place the discovery of coordinates and models on an
equal footing.Comment: 25 pages, 6 figures; added acknowledgment
Deep learning approach to Fourier ptychographic microscopy
Convolutional neural networks (CNNs) have gained tremendous success in
solving complex inverse problems. The aim of this work is to develop a novel
CNN framework to reconstruct video sequence of dynamic live cells captured
using a computational microscopy technique, Fourier ptychographic microscopy
(FPM). The unique feature of the FPM is its capability to reconstruct images
with both wide field-of-view (FOV) and high resolution, i.e. a large
space-bandwidth-product (SBP), by taking a series of low resolution intensity
images. For live cell imaging, a single FPM frame contains thousands of cell
samples with different morphological features. Our idea is to fully exploit the
statistical information provided by this large spatial ensemble so as to make
predictions in a sequential measurement, without using any additional temporal
dataset. Specifically, we show that it is possible to reconstruct high-SBP
dynamic cell videos by a CNN trained only on the first FPM dataset captured at
the beginning of a time-series experiment. Our CNN approach reconstructs a
12800X10800 pixels phase image using only ~25 seconds, a 50X speedup compared
to the model-based FPM algorithm. In addition, the CNN further reduces the
required number of images in each time frame by ~6X. Overall, this
significantly improves the imaging throughput by reducing both the acquisition
and computational times. The proposed CNN is based on the conditional
generative adversarial network (cGAN) framework. Additionally, we also exploit
transfer learning so that our pre-trained CNN can be further optimized to image
other cell types. Our technique demonstrates a promising deep learning approach
to continuously monitor large live-cell populations over an extended time and
gather useful spatial and temporal information with sub-cellular resolution
Deep learning approach to Fourier ptychographic microscopy
Convolutional neural networks (CNNs) have gained tremendous success in solving complex inverse problems. The aim of this work is to develop a novel CNN framework to reconstruct video sequences of dynamic live cells captured using a computational microscopy technique, Fourier ptychographic microscopy (FPM). The unique feature of the FPM is its capability to reconstruct images with both wide field-of-view (FOV) and high resolution, i.e. a large space-bandwidth-product (SBP), by taking a series of low resolution intensity images. For live cell imaging, a single FPM frame contains thousands of cell samples with different morphological features. Our idea is to fully exploit the statistical information provided by these large spatial ensembles so as to make predictions in a sequential measurement, without using any additional temporal dataset. Specifically, we show that it is possible to reconstruct high-SBP dynamic cell videos by a CNN trained only on the first FPM dataset captured at the beginning of a time-series experiment. Our CNN approach reconstructs a 12800×10800 pixel phase image using only ∼25 seconds, a 50× speedup compared to the model-based FPM algorithm. In addition, the CNN further reduces the required number of images in each time frame by ∼ 6×. Overall, this significantly improves the imaging throughput by reducing both the acquisition and computational times. The proposed CNN is based on the conditional generative adversarial network (cGAN) framework. We further propose a mixed loss function that combines the standard image domain loss and a weighted Fourier domain loss, which leads to improved reconstruction of the high frequency information. Additionally, we also exploit transfer learning so that our pre-trained CNN can be further optimized to image other cell types. Our technique demonstrates a promising deep learning approach to continuously monitor large live-cell populations over an extended time and gather useful spatial and temporal information with sub-cellular resolution.We would like to thank NVIDIA Corporation for supporting us with the GeForce Titan Xp through the GPU Grant Program. (NVIDIA Corporation; GeForce Titan Xp through the GPU Grant Program)First author draf
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