اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدSNODE: Spectral Discretization of Neural ODEs for System Identification
96
0
0.0
(
0
)
نشر من قبل
Alessio Quaglino PhD
تاريخ النشر
2019
مجال البحث
الهندسة المعلوماتية
والبحث باللغة
English
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
This paper proposes the use of spectral element methods citep{canuto_spectral_1988} for fast and accurate training of Neural Ordinary Differential Equations (ODE-Nets; citealp{Chen2018NeuralOD}) for system identification. This is achieved by expressing their dynamics as a truncated series of Legendre polynomials. The series coefficients, as well as the network weights, are computed by minimizing the weighted sum of the loss function and the violation of the ODE-Net dynamics. The problem is solved by coordinate descent that alternately minimizes, with respect to the coefficients and the weights, two unconstrained sub-problems using standard backpropagation and gradient methods. The resulting optimization scheme is fully time-parallel and results in a low memory footprint. Experimental comparison to standard methods, such as backpropagation through explicit solvers and the adjoint technique citep{Chen2018NeuralOD}, on training surrogate models of small and medium-scale dynamical systems shows that it is at least one order of magnitude faster at reaching a comparable value of the loss function. The corresponding testing MSE is one order of magnitude smaller as well, suggesting generalization capabilities increase.
قيم البحث
اقرأ أيضاً
To reduce random access memory (RAM) requirements and to increase speed of recognition algorithms we consider a weight discretization problem for trained neural networks. We show that an exponential discretization is preferable to a linear discretiza
tion since it allows one to achieve the same accuracy when the number of bits is 1 or 2 less. The quality of the neural network VGG-16 is already satisfactory (top5 accuracy 69%) in the case of 3 bit exponential discretization. The ResNet50 neural network shows top5 accuracy 84% at 4 bits. Other neural networks perform fairly well at 5 bits (top5 accuracies of Xception, Inception-v3, and MobileNet-v2 top5 were 87%, 90%, and 77%, respectively). At less number of bits, the accuracy decreases rapidly.
Spurred by tremendous success in pattern matching and prediction tasks, researchers increasingly resort to machine learning to aid original scientific discovery. Given large amounts of observational data about a system, can we uncover the rules that
govern its evolution? Solving this task holds the great promise of fully understanding the causal interactions and being able to make reliable predictions about the systems behavior under interventions. We take a step towards answering this question for time-series data generated from systems of ordinary differential equations (ODEs). While the governing ODEs might not be identifiable from data alone, we show that combining simple regularization schemes with flexible neural ODEs can robustly recover the dynamics and causal structures from time-series data. Our results on a variety of (non)-linear first and second order systems as well as real data validate our method. We conclude by showing that we can also make accurate predictions under interventions on variables or the system itself.
We study the problem of sparse nonlinear model recovery of high dimensional compositional functions. Our study is motivated by emerging opportunities in neuroscience to recover fine-grained models of biological neural circuits using collected measure
ment data. Guided by available domain knowledge in neuroscience, we explore conditions under which one can recover the underlying biological circuit that generated the training data. Our results suggest insights of both theoretical and practical interests. Most notably, we find that a sign constraint on the weights is a necessary condition for system recovery, which we establish both theoretically with an identifiability guarantee and empirically on simulated biological circuits. We conclude with a case study on retinal ganglion cell circuits using data collected from mouse retina, showcasing the practical potential of this approach.
Despite having been studied to a great extent, the task of conditional generation of sequences of frames, or videos, remains extremely challenging. It is a common belief that a key step towards solving this task resides in modelling accurately both s
patial and temporal information in video signals. A promising direction to do so has been to learn latent variable models that predict the future in latent space and project back to pixels, as suggested in recent literature. Following this line of work and building on top of a family of models introduced in prior work, Neural ODE, we investigate an approach that models time-continuous dynamics over a continuous latent space with a differential equation with respect to time. The intuition behind this approach is that these trajectories in latent space could then be extrapolated to generate video frames beyond the time steps for which the model is trained. We show that our approach yields promising results in the task of future frame prediction on the Moving MNIST dataset with 1 and 2 digits.
Continuous deep learning architectures have recently re-emerged as Neural Ordinary Differential Equations (Neural ODEs). This infinite-depth approach theoretically bridges the gap between deep learning and dynamical systems, offering a novel perspect
ive. However, deciphering the inner working of these models is still an open challenge, as most applications apply them as generic black-box modules. In this work we open the box, further developing the continuous-depth formulation with the aim of clarifying the influence of several design choices on the underlying dynamics.
الأسئلة المقترحة
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
