**3. Intelligent systems for mathematical modeling**

My former advisor, George Stephanopoulos at MIT, was one of the first chemical engineers to systematically consider whether machines could help formulate

**27**

**Figure 4.**

*chemist dialect.*

*Mathematical Modeling: The Art of Translating between Minds and Machines…*

mathematical models. He called such machines intelligent systems for which he developed several modeling languages including MODEL.LA, a mathematical language to formulate process engineering models [5, 6]. He introduced a series of papers on formal modeling frameworks, intelligent systems in process engineering, and agent-based approaches for mathematical modeling [7, 8]. I had the pleasure to collaborate with a team of colleagues on one of his projects on a machine-assisted modeling approach entitled BatchDesignKit (BDK). BDK is a software architecture designed to interactively generate mathematical models [9–15]. It is composed of a batch sheet which features the formalized natural language input *chemist dialects* to define operational tasks as well as to allow the scheduling and sequencing of parallel and sequential tasks as they commonly used in chemical recipes of batch pharmaceutical plants. The example of **Figure 4** shows a typical batch sheet which lists operational tasks: "Charge a reactor by an amount of water and charge the same reactor with a chemical, then heat the system." As these batch sheets receive natural language commands from a chemist or chemical engineer, the equations describing the chemical operations are synthesized and solved inside the computer leading to new or purified process streams that evolve on the virtual computer reality as they would in the real chemistry lab. In accordance with the user interacting with BDK, the new batch recipe is refined in the virtual lab. The input of a chemical recipe in BDK is essentially identical to written instructions from a chemist's lab note book. To better inform users about the evolution of mathematical models for the synthesis of pharmaceutical compounds, BDK also generated a flowsheet which features a virtual representation of all processing units such as reactors or distillation columns, materials mixtures, compounds and phases as well as processing streams. Together, the batch sheet with its natural language input and the flowsheet for virtual representation of operational equipment and material streams constituted a virtual laboratory in which experiments could be conducted. **Figures 4** and **5** show an example of a batch sheet and a flowsheet as well as the name of operations that formulated that natural BDK input language, which constituted the vocabulary of a chemists' language. The intelligent

*BDK batch and flowsheet. Chemist can define batch process operation using natural language input in a* 

*DOI: http://dx.doi.org/10.5772/intechopen.83691*

*Mathematical Modeling: The Art of Translating between Minds and Machines… DOI: http://dx.doi.org/10.5772/intechopen.83691*

mathematical models. He called such machines intelligent systems for which he developed several modeling languages including MODEL.LA, a mathematical language to formulate process engineering models [5, 6]. He introduced a series of papers on formal modeling frameworks, intelligent systems in process engineering, and agent-based approaches for mathematical modeling [7, 8]. I had the pleasure to collaborate with a team of colleagues on one of his projects on a machine-assisted modeling approach entitled BatchDesignKit (BDK). BDK is a software architecture designed to interactively generate mathematical models [9–15]. It is composed of a batch sheet which features the formalized natural language input *chemist dialects* to define operational tasks as well as to allow the scheduling and sequencing of parallel and sequential tasks as they commonly used in chemical recipes of batch pharmaceutical plants. The example of **Figure 4** shows a typical batch sheet which lists operational tasks: "Charge a reactor by an amount of water and charge the same reactor with a chemical, then heat the system." As these batch sheets receive natural language commands from a chemist or chemical engineer, the equations describing the chemical operations are synthesized and solved inside the computer leading to new or purified process streams that evolve on the virtual computer reality as they would in the real chemistry lab. In accordance with the user interacting with BDK, the new batch recipe is refined in the virtual lab. The input of a chemical recipe in BDK is essentially identical to written instructions from a chemist's lab note book. To better inform users about the evolution of mathematical models for the synthesis of pharmaceutical compounds, BDK also generated a flowsheet which features a virtual representation of all processing units such as reactors or distillation columns, materials mixtures, compounds and phases as well as processing streams. Together, the batch sheet with its natural language input and the flowsheet for virtual representation of operational equipment and material streams constituted a virtual laboratory in which experiments could be conducted. **Figures 4** and **5** show an example of a batch sheet and a flowsheet as well as the name of operations that formulated that natural BDK input language, which constituted the vocabulary of a chemists' language. The intelligent



#### **Figure 4.**

*BDK batch and flowsheet. Chemist can define batch process operation using natural language input in a chemist dialect.*

*Technology, Science and Culture - A Global Vision*

chemical engineering senior design course. Development and analysis of the process flowsheet may take a student team operating the Aspen FlowSheet Software at the beginner's level about 45 man-hours, or 3 hours per week for 15 weeks. An expert user may be able to set up the flowsheet in only 10 hours. The third example concerns the development of a computational fluid mechanics (CFD) model, of which we will see more later in the study of the brain. Using commercial CFD software such as FLUENT [4], it may take a few days or weeks to set up a routine flow problem such as laminar flow in a cylindrical domain. A complex problem like subject-specific blood flow predictions such as an aneurysm may require 1–2 years of a PhD student. In biological systems, some CFD problems require even more than 2 years. The chart of **Figure 3** shows that in cost for model formulation falls in the range of a few hundred thousand dollars for junior level engineers; it may reach or exceed a half a million dollars if the modeling problem requires an expert such as a senior expert or a scientist. In contrast, the computational time for merely solving the mathematical model was calculated to amount to only \$500 of CPU time (=1 week cpu time). Accordingly, the cost of formulating models is much higher than the expense for solving mathematical equations. The expense for mathematical model-based learning stems mainly from the effort for problem formulation, a much smaller fraction is attributable to the solution on the computer. In a computationally intense scenario (=1 week CPU time), computational cost may accumulate about 10% of the cost. In the more complex modeling situation, the cost essentially lies mainly in the mathematical model formulation, interpretation, and testing of the system. It is therefore desirable to accelerate

*Overview of the cost of modeling. Problem formulation absorbs more than 90% of the cost for the development* 

**26**

**Figure 3.**

*of mathematical models.*

model generation and thus reduce its cost.

**3. Intelligent systems for mathematical modeling**

My former advisor, George Stephanopoulos at MIT, was one of the first chemical engineers to systematically consider whether machines could help formulate

#### **Figure 5.**

*List of operational tasks in the BDK batch for natural language input of chemical recipes (right). Flowsheet of batch operations and stream table for a batch recipe.*

BDK system was a model generation framework that used natural language input, synthesized equations, and created a virtual representation of materials and eventually solved these equations to predict the physiochemical state changes resulting from material transformations, phase separations, and reactions. The idea of using formal algorithms to support mathematical model generations has received attention in the community and continues to be an interesting research task in system science.
