Related papers: Deriving Analytical Solutions Using Symbolic Matri…
MATLAB(R) releases over the last 3 years have witnessed a continuing growth in the dynamic modeling capabilities offered by the System Identification Toolbox(TM). The emphasis has been on integrating deep learning architectures and training…
We describe a neural-based method for generating exact or approximate solutions to differential equations in the form of mathematical expressions. Unlike other neural methods, our system returns symbolic expressions that can be interpreted…
The pixel-wise dense prediction tasks based on weakly supervisions currently use Class Attention Maps (CAM) to generate pseudo masks as ground-truth. However, the existing methods typically depend on the painstaking training modules, which…
Dynamic causal modeling (DCM) is a Bayesian framework to infer directed connections between compartments, and has been used to describe the interactions between underlying neural populations based on functional neuroimaging data. DCM is…
Symbolic data analysis (SDA) is an emerging area of statistics concerned with understanding and modelling data that takes distributional form (i.e. symbols), such as random lists, intervals and histograms. It was developed under the premise…
Neither deep neural networks nor symbolic AI alone has approached the kind of intelligence expressed in humans. This is mainly because neural networks are not able to decompose joint representations to obtain distinct objects (the so-called…
This paper studies the semi-analytic solution (SAS) of a power system's differential-algebraic equation. A SAS is a closed-form function of symbolic variables including time, the initial state and the parameters on system operating…
Symbolic regression is a machine learning technique that can learn the governing formulas of data and thus has the potential to transform scientific discovery. However, symbolic regression is still limited in the complexity and…
Mathematical modeling is now used commonly in the analysis of signaling networks. With advances in high resolution microscopy, the spatial location of different signaling molecules and the spatio-temporal dynamics of signaling microdomains…
We developed a novel approach to identification and model testing in linear structural equation models (SEMs) based on auxiliary variables (AVs), which generalizes a widely-used family of methods known as instrumental variables. The…
Explainable AI aims to render model behavior understandable by humans, which can be seen as an intermediate step in extracting causal relations from correlative patterns. Due to the high risk of possible fatal decisions in image-based…
Vector Symbolic Architectures (VSAs) are one approach to developing Neuro-symbolic AI, where two vectors in $\mathbb{R}^d$ are `bound' together to produce a new vector in the same space. VSAs support the commutativity and associativity of…
Similarity measures are widely used to interpret the representational geometries used by neural networks to solve tasks. Yet, because existing methods compare the extrinsic geometry of representations in state space, rather than their…
Symbolic models or abstractions are known to be powerful tools for the control design of cyber-physical systems (CPSs) with logic specifications. In this paper, we investigate a novel learning-based approach to the construction of symbolic…
Symbolic Data Analysis (SDA) is a relatively new field of statistics that extends conventional data analysis by taking into account intrinsic data variability and structure. Unlike conventional data analysis, in SDA the features…
Symbolic Regression (SR) offers an interpretable alternative to conventional Machine-Learning (ML) approaches, which are often criticized as ``black boxes''. In contrast to standard regression models that require a prescribed functional…
The research area of Networked Control Systems (NCS) has been the topic of intensive study in the last decade. In this paper we give a contribution to this research line by addressing symbolic control design of (possibly unstable) nonlinear…
Carbon isotope labeling method is a standard metabolic engineering tool for flux quantification in living cells. To cope with the high dimensionality of isotope labeling systems, diverse algorithms have been developed to reduce the number…
We investigate the use of machine learning for solving analytic problems in theoretical physics. In particular, symbolic regression (SR) is making rapid progress in recent years as a tool to fit data using functions whose overall form is…
Recent work on Neural-Symbolic systems that learn the discrete planning model from images has opened a promising direction for expanding the scope of Automated Planning and Scheduling to the raw, noisy data. However, previous work only…