M any systems of primary interest in biology and in engineering can be seen as analog networks. An analog network (igure 1) is composed of a collection of nodes representing devices and a collection of directed or undirected links connecting the devices and having a connection strength repre- sented by a numerical value. To illustrate the idea of analog networks and explain the practical importance of their automat- ed synthesis and reverse engineering, we consider three examples: analog electron- ic circuits, artiicial neural networks, and genetic regulatory networks. An analog electronic circuit is a collec- tion of interconnected electronic devices such as transistors, diodes, capacitors, and resistors (igure 2). The purpose of an ana- log electronic circuit is the production and processing of electrical signals whose amplitude can vary continuously in time. This is opposed to digital circuits, which process signals whose amplitude is dis- cretized. Despite a steady trend towards the substitution of analog with digital sig- nal processing, analog circuits maintain a crucial role in electronic design. For exam- ple, in many applications, analog elec- tronic circuits are required in order to con- nect digital circuits to continuous input and output signals; these analog circuits have a profound impact on overall system performance. There is therefore a well- founded interest in the automation of the design of analog electronic circuits. How- ever, analog design has proved much more dificult to automate than digital design. To understand the nature of this dificul- ty, one must consider that the function realized by an electronic circuit is deter- mined by two aspects: its topology and its sizing. The topology of a circuit refers to the nature of the devices that compose the circuit and how they are connected together. The sizing of a circuit refers to the values of the numerical parameters that characterize the devices and links. An example of a numerical parameter of a device is the capacitance of a capacitor. As mentioned above, the numerical parame- ter associated with a link corresponds to the interaction strength between the devices it connects. In the case of elec- tronic circuits, the interaction strength between two devices is inversely propor- tional to the resistance between them. A zero resistance value corresponds to a direct connection and realizes the maxi- mum connection strength. An ininite resistance corresponds to the absence of a link connecting the two devices. All other resistance values correspond to the pres- ence of a link with a resistor between the devices and realize intermediate connec- tion strengths. In digital circuits, only the two extreme values of connection strength are used to connect the devices (for example, logic gates) that constitute the circuit. In analog electronic circuits, in contrast, a large variety of connection strengths are typically required to achieve the intended functionality. This means that, compared to a digital designer, an analog designer must take into account a Articles FALL 2008 63 Copyright © 2008, Association for the Advancement of Artiicial Intelligence. All rights reserved. ISSN 0738-4602 The Age of Analog Networks Claudio Mattiussi, Daniel Marbach, Peter Dürr, and Dario Floreano ■ A large class of systems of biological and technological relevance can be described as analog networks, that is, col- lections of dynamic devices interconnected by links of varying strength. Some exam- ples of analog networks are genetic regula- tory networks, metabolic networks, neural networks, analog electronic circuits, and control systems. Analog networks are typ- ically complex systems that include non- linear feedback loops and possess tempo- ral dynamics at different time scales. Both the synthesis and reverse engineering of analog networks are recognized as knowl- edge-intensive activities, for which few systematic techniques exist. In this paper we will discuss the general relevance of the analog network concept and describe an evolutionary approach to the automatic synthesis and the reverse engineering of analog networks. The proposed approach is called analog genetic encoding (AGE) and realizes an implicit genetic encoding of analog networks. AGE permits the evo- lution of human-competitive solutions to real-world analog network design and identiication problems. This is illustrated by some examples of application to the design of electronic circuits, control sys- tems, learning neural architectures, and the reverse engineering of biological net- works.